GAP Manual: 12.7. Field Functions for Rationals

As was already mentioned in the introduction of this chapter the GAP object Rationals is the field of all rationals. All field functions, e.g., Norm and MinPol are applicable to this domain and its elements. However, since the field of rationals is the prime field, all those functions are trivial. Therefore, Conjugates( Rationals, q ) returns [ q ], Norm( Rationals, q ) and Trace( Rationals, q ) return q, and CharPol( Rationals, q ) and MinPol( Rationals, q ) both return [ -q, 1 ].