Bill Allombert on Tue, 13 Dec 2005 10:52:23 +0100 |
[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]
Re: Splitting fields |
On Tue, Dec 13, 2005 at 10:16:48AM +0100, Jeroen Demeyer wrote: > Hello list, > > Suppose I have given an irreducible polynomial f(x) in Z[x]. > I want to use PARI/GP to find the splitting field (as a nf) of this > polynomial, i.e. the smallest field containing *all* roots of f(x). > > The problem is that Q[x]/f(x) is not equal to the splitting field if > it's not Galois. For instance, the splitting field of x^3 - 2 has degree 6. > > Is there a way to do this? Sure, but beware that the splitting field is generally of very large degree hence not practical to use. There are several way to compute it; The simplest is to use polcompositum, for example: split(f)= { local(V,F1,F2); F1=f;F2=0; until(poldegree(F1)==poldegree(F2), F2=F1; V=polcompositum(F1,f);F1=V[#V]); F1 } Cheers, Bill.