Just wondering
Does there exist an algorithm that can determine in a finite number of steps whether a polynomial over $ℚ$ is irreducible over $ℚ$?
I know there are algorithms, but is there one that works with all polynomials over $ℚ$?
2026-04-09 12:38:36.1775738316
Is there an algorithm to figure out whether a certain polynomial over $ℚ$ is irreducible or not?
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Yes, such as Kronecker's method and the Zassenhaus algorithm. However, such algorithms usually perform full factorization. See Wikipedia.