Carlo Wood on Mon, 28 Apr 2008 15:24:03 +0200 |
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How to check irreducibility over a finite field? |
Hi, I'd like to check the irredicubility of a given polynomial over a field K. 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? -- Carlo Wood <carlo@alinoe.com>