MHB How can I determine a polynomial is irreducible in C？

[Nonad]

Hello!(Blush)

I learned about Eisenstein's irreducibility criterion. But it's still hard for me to implement it when the integer coefficients may be as larger as 1e9.
What's more, how can I (or my computer?) know when to change x into x+a?

It really puzzles me()??

 

[I like Serena]

Hello!

I learned about Eisenstein's irreducibility criterion. But it's still hard for me to implement it when the integer coefficients may be as larger as 1e9.

Welcome to MHB Nonad! (Wave)

What is the problem with such large coefficients?
If we use a [m]int64_t[/m] we support up to [m]9e18[/m].
It may become more problematic to verify primality of integers within a reasonable time, but there are some optimizations that can be done there.

What's more, how can I (or my computer?) know when to change x into x+a?

It really puzzles me()??

If the criterion is satisfied, we are done.
If it is not, then the result is inconclusive.
Shifting with $x+a$, or reversing coefficients will not necessarily lead to a conclusive result.
It is just something to try so that we get conclusive results in more cases.
I'm not aware yet of a heuristic how to pick $a$.
We might simply try every $a$ from $1$ up to the highest coefficient or some such.

 

[Nonad]

It is just something to try so that we get conclusive results in more cases.
I'm not aware yet of a heuristic how to pick $a$.
We might simply try every $a$ from $1$ up to the highest coefficient or some such.

Thank you very much(Blush)
Yes, you are right. I have to enumerate using Eisenstein's irreducibility criterion.
It's not acceptable for my task which includes large data and, as a sufficient condition, it may provide wrong answers.
Finally, we implemented Factorization theorem of real coefficient polynomials to solve the problem.

Thanks again(Smile)