README.md example is broken

[fingolfin]

I wanted to update the README.md example to match the current "reality". Unfortunately, it seems to have been broken by the modules changes by @AlexD97 and @jankoboehm (CC @fieker). I am now getting this:

julia> k, a = quadratic_field(-5)
(Imaginary quadratic field defined by x^2 + 5, sqrt(-5))

julia> zk = maximal_order(k)
Maximal order of Imaginary quadratic field defined by x^2 + 5
with basis nf_elem[1, sqrt(-5)]

julia> factorisations(zk(6))
2-element Vector{Fac{NfOrdElem}}:
 -1 * (sqrt(-5) + 1) * (sqrt(-5) - 1)
 -1 * 2 * -3

julia> Qx, x = PolynomialRing(QQ, [:x1,:x2])
(Multivariate Polynomial Ring in x1, x2 over Rational Field, fmpq_mpoly[x1, x2])

julia> R = grade(Qx, [1,2])[1]
Multivariate Polynomial Ring in x1, x2 over Rational Field graded by
  x1 -> [1]
  x2 -> [2]

julia> f = R(x[1]^2+x[2])
x1^2 + x2

julia> degree(f)
graded by [2]

julia> F = FreeModule(R, 1)
Free module of rank 1 over R

julia> s = sub(F, [f*F[1]])
(Submodule over R with 1 generator and no relations
, Module homomorphism with
Domain: Submodule over R with 1 generator and no relations

Codomain: F)

julia> H, mH = hom(s, quo(F, s))
ERROR: MethodError: no method matching quo(::AbstractAlgebra.Generic.FreeModule{MPolyElem_dec{fmpq, fmpq_mpoly}}, ::Tuple{AbstractAlgebra.Generic.Submodule{MPolyElem_dec{fmpq, fmpq_mpoly}}, AbstractAlgebra.Generic.ModuleHomomorphism{MPolyElem_dec{fmpq, fmpq_mpoly}}})
Closest candidates are:
  quo(::S, ::Hecke.AbsAlgAssIdl{S, T, U}) where {S, T, U} at ~/.julia/packages/Hecke/M7nVW/src/AlgAss/Ideal.jl:428
  quo(::AbstractAlgebra.FPModule{T}, ::AbstractAlgebra.FPModule{T}) where T<:RingElement at ~/.julia/packages/AbstractAlgebra/KPT2D/src/QuotientModule.jl:22
Stacktrace:
 [1] top-level scope
   @ REPL[11]:1

Perhaps PR #1021 helps ? I didn't try yet.

[thofma]

It must be free_module instead of FreeModule. But it ultimately shows that we now have plenty of free module implementations with incompatible APIs.

[AlexD97]

Yes, it must be free_module or FreeMod instead of FreeModule. #1021 doesn't help here. The problem is (as pointed out) that there are incompatible free module types.

[fingolfin]

There is another problem, grading_group(H) fails (for details, see PR #1044)