Timeline for Algorithms to find irreducible polynomials of a given degree
Current License: CC BY-SA 3.0
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| Aug 26, 2012 at 16:22 | comment | added | Will Sawin | This polynomial will be the product of the elementary cyclotomic polynomials $\phi_k(x)$ for $k|p^{dn}-1$ but $k\not | p^{en}-1$ for $e<d$. This is true because each $x^{p^{en}}-x$ factors into a product of elementary cyclotomic polynomials so a polynomial computed from them by inclusion-exclusion does as well, and the elementary cyclotomic polynomials involved, since $p$ does not divide the order of their roots, are still relatively prime mod $p$, so we can easily check which ones are included in the product of ell irreducible polynomilas of degree $d$. | |
| Aug 26, 2012 at 16:13 | history | answered | Felipe Voloch | CC BY-SA 3.0 |