Irreducibility and reducibility [closed]Methods to see if a polynomial is irreducibleProve that the polynomial $x^5+2x+1$ is irreducible over $mathbbZ$.Show that a polynomial is irreducible in $mathbbQ$Prove irreducibility of a polynomialIrreducibility of a particular polynomialIrreducible polynomials of the form $x^n - q$Irreducibility criteria for polynomials with several variables.Using Dedekind's prime ideal factorisation theoremirreducibility of x^m-aChecking Polynomial ReducibilityIrreducibility of the following Polynomial over $mathbbQ$Applying degree 2 or 3 irreducibility tests to higher degree
Need help understanding what a natural log transformation is actually doing and why specific transformations are required for linear regression
What should you do when eye contact makes your subordinate uncomfortable?
What is Cash Advance APR?
Is there a RAID 0 Equivalent for RAM?
Can I still be respawned if I die by falling off the map?
Why does a simple loop result in ASYNC_NETWORK_IO waits?
What are the advantages of simplicial model categories over non-simplicial ones?
Calculating total slots
Does an advisor owe his/her student anything? Will an advisor keep a PhD student only out of pity?
Can disgust be a key component of horror?
Does Doodling or Improvising on the Piano Have Any Benefits?
Fear of getting stuck on one programming language / technology that is not used in my country
Is aluminum electrical wire used on aircraft?
Quoting Keynes in a lecture
Lowest total scrabble score
Picking the different solutions to the time independent Schrodinger eqaution
Non-trope happy ending?
How does the math work for Perception checks?
How to explain what's wrong with this application of the chain rule?
Recommended PCB layout understanding - ADM2572 datasheet
Extract more than nine arguments that occur periodically in a sentence to use in macros in order to typset
What is the evidence for the "tyranny of the majority problem" in a direct democracy context?
Using substitution ciphers to generate new alphabets in a novel
It grows, but water kills it
Irreducibility and reducibility [closed]
Methods to see if a polynomial is irreducibleProve that the polynomial $x^5+2x+1$ is irreducible over $mathbbZ$.Show that a polynomial is irreducible in $mathbbQ$Prove irreducibility of a polynomialIrreducibility of a particular polynomialIrreducible polynomials of the form $x^n - q$Irreducibility criteria for polynomials with several variables.Using Dedekind's prime ideal factorisation theoremirreducibility of x^m-aChecking Polynomial ReducibilityIrreducibility of the following Polynomial over $mathbbQ$Applying degree 2 or 3 irreducibility tests to higher degree
$begingroup$
Is there is any universal method or law which can be applied to check reducibility and irreducibility of a given polynomial in $mathbbQ[X]$?
algebraic-number-theory factoring polynomial-rings
edited Mar 15 at 4:33
Seewoo Lee
7,124927
asked Mar 15 at 4:19
Jayantha S BhatJayantha S Bhat
61
$endgroup$
closed as off-topic by Jyrki Lahtonen, Lord Shark the Unknown, mrtaurho, Vinyl_cape_jawa, Shaun Mar 15 at 13:53
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Jyrki Lahtonen, mrtaurho, Vinyl_cape_jawa, Shaun
add a comment |
$begingroup$
Is there is any universal method or law which can be applied to check reducibility and irreducibility of a given polynomial in $mathbbQ[X]$?
algebraic-number-theory factoring polynomial-rings
edited Mar 15 at 4:33
Seewoo Lee
7,124927
asked Mar 15 at 4:19
Jayantha S BhatJayantha S Bhat
61
$endgroup$
closed as off-topic by Jyrki Lahtonen, Lord Shark the Unknown, mrtaurho, Vinyl_cape_jawa, Shaun Mar 15 at 13:53
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Jyrki Lahtonen, mrtaurho, Vinyl_cape_jawa, Shaun
2
$begingroup$
Check out factorization based on LLL. Mind you, the question is more than a bit lacking of context, so it is impossible to gauge what level of tools will help you. Study our guide for new askers and fix the post, please. Also, compendiums of factorization methods/irreducibility tests have been covered already on our site. So the question may easily be a duplicate. Did you search the site at all?
$endgroup$
– Jyrki Lahtonen
Mar 15 at 4:30
$begingroup$
Sorry for the inconvenience and also thank you..
$endgroup$
– Jayantha S Bhat
Mar 15 at 4:52
1
$begingroup$
No inconvenience, really. There is a learning curve in getting up to speed with the site culture. I could (should!) have phrased my comment better. After all, when answering a question well requires writing a book, which may be the case here :-), we could also classify the question as too broad. The simple answer is that there is no simple check guaranteed to give you a definite test one way or the other. There are several tricks that may or may not work well for a given polynomial. Some are described in this example.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:20
1
$begingroup$
For something more comprehensive check out this.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:22
add a comment |
$begingroup$
Is there is any universal method or law which can be applied to check reducibility and irreducibility of a given polynomial in $mathbbQ[X]$?
algebraic-number-theory factoring polynomial-rings
edited Mar 15 at 4:33
Seewoo Lee
7,124927
asked Mar 15 at 4:19
Jayantha S BhatJayantha S Bhat
61
$endgroup$
Is there is any universal method or law which can be applied to check reducibility and irreducibility of a given polynomial in $mathbbQ[X]$?
algebraic-number-theory factoring polynomial-rings
algebraic-number-theory factoring polynomial-rings
edited Mar 15 at 4:33
Seewoo Lee
7,124927
asked Mar 15 at 4:19
Jayantha S BhatJayantha S Bhat
61
edited Mar 15 at 4:33
Seewoo Lee
7,124927
asked Mar 15 at 4:19
Jayantha S BhatJayantha S Bhat
61
edited Mar 15 at 4:33
Seewoo Lee
7,124927
edited Mar 15 at 4:33
Seewoo Lee
7,124927
edited Mar 15 at 4:33
Seewoo Lee
7,124927
7,124927
asked Mar 15 at 4:19
Jayantha S BhatJayantha S Bhat
61
asked Mar 15 at 4:19
Jayantha S BhatJayantha S Bhat
61
asked Mar 15 at 4:19
Jayantha S BhatJayantha S Bhat
61
61
closed as off-topic by Jyrki Lahtonen, Lord Shark the Unknown, mrtaurho, Vinyl_cape_jawa, Shaun Mar 15 at 13:53
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Jyrki Lahtonen, mrtaurho, Vinyl_cape_jawa, Shaun
closed as off-topic by Jyrki Lahtonen, Lord Shark the Unknown, mrtaurho, Vinyl_cape_jawa, Shaun Mar 15 at 13:53
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Jyrki Lahtonen, mrtaurho, Vinyl_cape_jawa, Shaun
2
$begingroup$
Check out factorization based on LLL. Mind you, the question is more than a bit lacking of context, so it is impossible to gauge what level of tools will help you. Study our guide for new askers and fix the post, please. Also, compendiums of factorization methods/irreducibility tests have been covered already on our site. So the question may easily be a duplicate. Did you search the site at all?
$endgroup$
– Jyrki Lahtonen
Mar 15 at 4:30
$begingroup$
Sorry for the inconvenience and also thank you..
$endgroup$
– Jayantha S Bhat
Mar 15 at 4:52
1
$begingroup$
No inconvenience, really. There is a learning curve in getting up to speed with the site culture. I could (should!) have phrased my comment better. After all, when answering a question well requires writing a book, which may be the case here :-), we could also classify the question as too broad. The simple answer is that there is no simple check guaranteed to give you a definite test one way or the other. There are several tricks that may or may not work well for a given polynomial. Some are described in this example.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:20
1
$begingroup$
For something more comprehensive check out this.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:22
add a comment |
2
$begingroup$
Check out factorization based on LLL. Mind you, the question is more than a bit lacking of context, so it is impossible to gauge what level of tools will help you. Study our guide for new askers and fix the post, please. Also, compendiums of factorization methods/irreducibility tests have been covered already on our site. So the question may easily be a duplicate. Did you search the site at all?
$endgroup$
– Jyrki Lahtonen
Mar 15 at 4:30
$begingroup$
Sorry for the inconvenience and also thank you..
$endgroup$
– Jayantha S Bhat
Mar 15 at 4:52
1
$begingroup$
No inconvenience, really. There is a learning curve in getting up to speed with the site culture. I could (should!) have phrased my comment better. After all, when answering a question well requires writing a book, which may be the case here :-), we could also classify the question as too broad. The simple answer is that there is no simple check guaranteed to give you a definite test one way or the other. There are several tricks that may or may not work well for a given polynomial. Some are described in this example.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:20
1
$begingroup$
For something more comprehensive check out this.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:22
2
2
$begingroup$
Check out factorization based on LLL. Mind you, the question is more than a bit lacking of context, so it is impossible to gauge what level of tools will help you. Study our guide for new askers and fix the post, please. Also, compendiums of factorization methods/irreducibility tests have been covered already on our site. So the question may easily be a duplicate. Did you search the site at all?
$endgroup$
– Jyrki Lahtonen
Mar 15 at 4:30
$begingroup$
Check out factorization based on LLL. Mind you, the question is more than a bit lacking of context, so it is impossible to gauge what level of tools will help you. Study our guide for new askers and fix the post, please. Also, compendiums of factorization methods/irreducibility tests have been covered already on our site. So the question may easily be a duplicate. Did you search the site at all?
$endgroup$
– Jyrki Lahtonen
Mar 15 at 4:30
$begingroup$
Sorry for the inconvenience and also thank you..
$endgroup$
– Jayantha S Bhat
Mar 15 at 4:52
$begingroup$
Sorry for the inconvenience and also thank you..
$endgroup$
– Jayantha S Bhat
Mar 15 at 4:52
1
1
$begingroup$
No inconvenience, really. There is a learning curve in getting up to speed with the site culture. I could (should!) have phrased my comment better. After all, when answering a question well requires writing a book, which may be the case here :-), we could also classify the question as too broad. The simple answer is that there is no simple check guaranteed to give you a definite test one way or the other. There are several tricks that may or may not work well for a given polynomial. Some are described in this example.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:20
$begingroup$
No inconvenience, really. There is a learning curve in getting up to speed with the site culture. I could (should!) have phrased my comment better. After all, when answering a question well requires writing a book, which may be the case here :-), we could also classify the question as too broad. The simple answer is that there is no simple check guaranteed to give you a definite test one way or the other. There are several tricks that may or may not work well for a given polynomial. Some are described in this example.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:20
1
1
$begingroup$
For something more comprehensive check out this.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:22
$begingroup$
For something more comprehensive check out this.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:22
add a comment |
0
active
oldest
votes
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
2
$begingroup$
Check out factorization based on LLL. Mind you, the question is more than a bit lacking of context, so it is impossible to gauge what level of tools will help you. Study our guide for new askers and fix the post, please. Also, compendiums of factorization methods/irreducibility tests have been covered already on our site. So the question may easily be a duplicate. Did you search the site at all?
$endgroup$
– Jyrki Lahtonen
Mar 15 at 4:30
$begingroup$
Sorry for the inconvenience and also thank you..
$endgroup$
– Jayantha S Bhat
Mar 15 at 4:52
1
$begingroup$
No inconvenience, really. There is a learning curve in getting up to speed with the site culture. I could (should!) have phrased my comment better. After all, when answering a question well requires writing a book, which may be the case here :-), we could also classify the question as too broad. The simple answer is that there is no simple check guaranteed to give you a definite test one way or the other. There are several tricks that may or may not work well for a given polynomial. Some are described in this example.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:20
1
$begingroup$
For something more comprehensive check out this.
$endgroup$
– Jyrki Lahtonen
Mar 15 at 5:22