To compute the abstract class group I can just create a number field K = QuadraticField(-23) and ask for it K.class_group() -> Multiplicative Abelian Group isomorphic to C3 Is there a way to obtain representatives of the ideal classes (like in Magma where there is a second return value that is a map from the abstract group to the set of prime ideals? When trying to obtain generators "by hand" I encountered the following problem: p = K.factor_integer(2)[0][0] is a prime divisor of 2, which happens to have order 3 (the function p.order() is not implemented yet). p.is_principal() -> False However: (p^3).is_principal() -> False gives the wrong answer. This roundabout gives the correct answer len((p^3).gens_reduced()) == 1 -> True but I encountered instances where the reduced set of generators is not as reduced as it could be, so this is not a reliable method.
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