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/sci/ - Science & Math

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11551072 No.11551072 [Reply] [Original]

What's the easiest way to know if a given polynomial is irreducible?

>> No.11551080

>>11551072
Coffee isn't good for you.

>> No.11551089

>>11551072
Eisenstein criterion.

>> No.11551101
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11551101

>> No.11551108

>>11551072

probably eisenstein

>> No.11551116

>>11551072
Say it is, in an contrarian or insulting way, accompanied with a brainlet wojak and post it on /sci/

>> No.11551118

>>11551072
division

>> No.11551197

>>11551072
There really isn't a pretty and efficient way of doing it. Eisenstein criteria is the best you can hope in terms of easiness of use, I guess.
What you could do is computing the Galois group and seeing if it is transitive on {1,2,...,n} (n being the polynomial's degree).
There are algorithms to determine the Galois group of a polynomial, but they aren't nice to do by hand.

>> No.11551224

>>11551072
Over which field? If [math]\mathbb{C}[/math] then check its degree.

>> No.11551231

If the orders less than 4 you can check if it's reducible in in the integers modulo some prime... so sometimes it's really easy to check for reducability

>> No.11552429

>>11551224
GF(2). I guess i can use Newton's polygon too?

>> No.11552567

>>11551072
>depends on what ring the polynomial is over

>> No.11552665

I wanna learn more about Polynomials, tell me how, /sci/.