|Bill Allombert on Mon, 28 Apr 2008 18:47:31 +0200|
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|Re: How to check irreducibility over a finite field?|
On Mon, Apr 28, 2008 at 03:23:40PM +0200, Carlo Wood wrote: > Hi, > > I'd like to check the irredicubility of a given > polynomial over a field K. Please note that there is a function polisirreducible for that purpose. > Let K = F_2[t]/r(t)F_2[t], where r(t) is a given > reduction polynomial over F_2. > > Let L = K[s]/u(s)K[s], where u(s) is a given > reduction polynomial over K. > > I want to manually pick a u(s) and then check > if I can factor it in K. > > Here is what I tried: > > First I define r(t): > > ? r = Mod(1,2)*t^6 + Mod(1,2)*t + Mod(1,2); > > It is possible to check that this is irreducible over F_2 with: > > ? lift(factormod(r, 2)) > %2 = > [t^6 + t + 1 1] > > Next, I define a u(s): > > ? u = Mod(Mod(1,2),r)*s^2 + Mod(Mod(1,2),r)*s + Mod(Mod(1,2),r); > > Now I want to see if I can factor this over K: > > ? lift(factormod(u, r)) > *** factormod: incorrect type in factmod. > > Not even this works: > > ? lift(factormod(u, 2)) > *** factormod: incorrect type in factmod. > > How can I factor a polynomial u(s) over K? Use factor(u) or factorff(u,2,r) if the moduli are implicit. Cheers, Bill.