Add preimage and kernel functionality to BQFClassGroupQuotientMorphism - #42676
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Add preimage and kernel functionality to BQFClassGroupQuotientMorphism#42676TheBlupper wants to merge 2 commits into
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Extend
BQFClassGroupQuotientMorphismto now provide a subgroup for the kernel, and to allow finding a preimage of any class in the codomain. The algorithms are somewhat cobbled together from different sources, SCALLOP gives a nice exposition of the kernel structure, but the concrete implementation of it I had to figure out myself.I have not seen a description of this preimage algorithm elsewhere, which doesn't require the factorization of the index (or relative conductor, don't know which term I like more).
Some previous discussion on this topic #40143 (comment), where the SCALLOP paper was reccomended by @yyyyx4.
A slightly unrelated issue I noticed, that is not yet addressed here, is that
sage.rings.number_field.order::quadratic_order_class_number(which is used byBQFClassGroup.order()) is very slow when the fundamental discriminant is very small but the conductor is large. This should not be the case, as the class number h(f^2*D) can be easily computed from h(D) using these kernel formulas.📝 Checklist
⌛ Dependencies