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Computational algebraic number theory

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A small change to allow this: ``` julia> G = abelian_group([3, 0]); julia> N = matrix(FlintZZ, 2, 1, [ 1, 1 ]); julia> G(N) Element of GrpAb: Z/3 x Z...

This change makes the code in https://github.com/oscar-system/Oscar.jl/issues/2915#issuecomment-1801794028 run. And I find it nice to have for consistency (see https://github.com/oscar-system/Oscar.jl/issues/2915#issuecomment-1801794028).

Qx, x = QQ["x"]; K, a = number_field(Qx([-881539931206823616,457325902411822080,16029750347584272,-124243211029392,-1536813216432,10162275552,33311655,-246753,0,1]), "a", cached = false); OK = maximal_order(K); P = prime_ideals_over(OK, 2)[1]; pi = uniformizer(P); el = FacElem(K, Dict{AbsSimpleNumFieldElem, ZZRingElem}(-70023594813717393//2617723003857817722429670559599034368*a^8 - 10407880684532886175//3926584505786726583644505839398551552*a^7 +...

Draft until I finish the benchmarking and the final polishing. Comments and suggestions are welcome. The `testfile.jl` file is temporary: I use it to test the `save_partial` part.

There is `Hecke.factor` and `AbstractAlgebra/Nemo.factor`. Both of them have the other one as a fallback, see: https://github.com/thofma/Hecke.jl/blob/bb9dbe60f8c7da4eb4f490b5d8fdfdeb690c3eb5/src/Hecke.jl#L223 https://github.com/thofma/Hecke.jl/blob/f96fb3b2cca05bbbf7a9d579e9c615cc0baed302/src/Misc/Integer.jl#L179 This has the drawback that for types, where `factor` is not supported...

Type renamings in #1376. ## Number field related | old/current name | new name | |-----------------------|----------| | AnticNumberField | AbsSimpleNumField | | nf_elem | AbsSimpleNumFieldElem | | NfAbsNS | AbsNonSimpleNumField...

I am writing down new names for the types related to groups: https://hackmd.io/ONVPdlfARgWzkfkNkcJkgA?both#Something-with-groups I would appreciate some help with it @ThomasBreuer @fingolfin @fieker. I guess we can live with `FinGenGrpAb`?...

This is to be able to create Modules in Oscar over non-commutative rings, as discussed with @HechtiDerLachs and @fieker

``` julia> basis_matrix(0 * maximal_order(quadratic_field(-1)[1])) [0 0] [0 0] julia> basis(0 * maximal_order(quadratic_field(-1)[1])) 2-element Vector{NfOrdElem}: 0 0 ``` This does not make much sense. P.S.: Magma does the "right" thing.

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