  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  [33X[0;0YA  number  field  is  a  finite  extension of the field of rational numbers.
  [5XAlnuth[105X  provides  various  methods  to  compute with number fields which are
  given  by  a  defining polynomial or by generators. For background on number
  fields we refer to [ST79].[133X
  
  [33X[0;0YSome  of  the  methods provided in this package are written in [5XGAP[105X code. The
  other  part  of  the  methods  is imported from the Computer Algebra Systems
  PARI/GP  [PAR11]  respectively  OSCAR  [DEF+25], [OSC24]. Hence this package
  contains  some  [5XGAP[105X  functions  and  an interface to some functions to these
  computer  algebra  systems.  Therefore  one  has  to  have  PARI/GP or OSCAR
  installed to use the full functionality of [5XAlnuth[105X.[133X
  
  [33X[0;0YWe  note  that  only a very small part of the functions available in PARI/GP
  respectively OSCAR are linked to [5XGAP[105X and they provides many more methods for
  computations in number fields.[133X
  
  [33X[0;0YThe  main methods included in [5XAlnuth[105X are: creating a number field, computing
  its  maximal order, computing its unit group and a presentation of this unit
  group,  computing  the  elements  of  a  given  norm  of  the  number field,
  determining a presentation for a finitely generated multiplicative subgroup,
  and  factoring  polynomials  defined  over  number fields. For background on
  algorithms for number fields we refer to [Poh93], [PZ89] and [Coh93].[133X
  
  [33X[0;0YThe  functions  provided  by [5XAlnuth[105X are introduced in the following chapter.
  Then an example application is outlined. In the final chapter of this manual
  the  installation  of  the  package  and  configuration  of  the  interface,
  including  hints  on  the  installation  of  PARI/GP respectively OSCAR, are
  described.[133X
  
