Faster class group computations using norm relations
Computing class groups
Goal : given a number field K, compute Cl(K).
Reminder : Buchmann’s algorithm.
I Choose S set of primes generating Cl(K) (GRH).
I Find S-units R ⊂ Z×
K,S.
I Compute C = ZS/hRi and U = ker(hRi → ZS).
I Check if hRi = Z×
K,S using class number formula.
I Output C.