Example FldNum_ClassGroupUnitGroup (H36E14)

In our field defined by x⁴ - 420 * x² + 40000, we obtain the class and unit groups as follows.

> R<x> := PolynomialRing(Integers());
> f := x^4 - 420*x^2 + 40000;
> K<y> := NumberField(f);
> C := ClassGroup(K);
> C;
Abelian Group of order 1
> U := UnitGroup(K);
> U;
Abelian Group isomorphic to Z/2 + Z + Z + Z
Defined on 4 generators
Relations:
      2*U.1 = 0
> T := TorsionUnitGroup(K);
> T;
Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
    2*T.1 = 0