Global Function Fields: Divisor class group

• Bounds on the generation of the class group
• Approximation of the class number
• Structure of the divisor class group, representation of divisor classes as abelian group elements
• S-class group, S-units and S-regulator for a finite set of places S
• Exact sequence
  
  $$0 \rightarrow U(S) \rightarrow F^\times \rightarrow Div(S) \rightarrow Cl(S) \rightarrow 0$$
  
  

• Image and preimage computation possible for the maps of the exact sequence
• Similar functionality for the finite maximal order
• p-rank of the divisor class group (separate method)

The development of this module is a joint project with the KANT group.