Timeline for Criteria for irreducibility of polynomial
Current License: CC BY-SA 3.0
3 events
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| Sep 4, 2012 at 6:56 | comment | added | Rurik | Thank you very much. As a matter of fact I think I managed: infact my 27 polynomials, even if scary-looking in the whole, turned out to be quite simple. For example, for many of them both $F$ and $G$ are of prime degree, and for the others, they have a degree written as the product of just to prime... this allowed me to esclude at once many decompositions... | |
| Aug 29, 2012 at 12:37 | comment | added | Michael Zieve | @Rurik: in practice, even if one only has partial or approximation information about two polynomials $F(x)$ and $G(x)$, one can usually prove that $F(x)-G(y)$ is irreducible. The reason is that one can usually show that both $F$ and $G$ are indecomposable, for instance just by writing $F = A \circ B$ where $A,B$ have undetermined coefficients, and then solving for the coefficients of $A$ and $B$. Once this has been done, then Fried's "same splitting field" result will imply irreducibility. Please feel free to email me about how to do this for your specific polynomials. | |
| Aug 29, 2012 at 12:23 | history | answered | Michael Zieve | CC BY-SA 3.0 |