[GAP Forum] Choosing the right Field...

[Ravi Kulkarni]

Dear GAP Forum,
  I am decomposing representations of finite groups and I find that I
need to keep track of the field the characters (or eigenvalues) take
values in.
  If I start with

  	R := PolynomialRing(Rationals,3);;

  I find that I should really have done

  	F := Field(Sqrt(3), E(4));;  	
	R := PolynomialRing(F,3);;

  instead, to get a nice decomposition in some example.
  Is there some way to do this automatically without explicitly
examining the eigenvalues/characters first?
  (And I think I now see why everybody tells me to work with
permutation groups instead of matrix representations - I think those
decompose over the Rationals only...)

  But I still would like to have a solution to my problem above... :)

  Thanks
    Ravi