Use padic_field/qadic_field and prepare deprecations

[joschmitt]

The "trivial" part of #1522.

[codecov]

Codecov Report

Attention: Patch coverage is 65.62500% with 11 lines in your changes missing coverage. Please review.

Project coverage is 75.80%. Comparing base (a98b156) to head (bf036cd).
Report is 10 commits behind head on master.

Files with missing lines	Patch %	Lines
src/LocalField/pAdic.jl	0.00%	3 Missing ⚠️
src/Deprecations.jl	0.00%	2 Missing ⚠️
src/LocalField/neq.jl	71.42%	2 Missing ⚠️
src/HeckeTypes.jl	50.00%	1 Missing ⚠️
src/LocalField/Conjugates.jl	80.00%	1 Missing ⚠️
src/LocalField/qAdic.jl	0.00%	1 Missing ⚠️
src/Misc/UnitsModM.jl	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1604      +/-   ##
==========================================
- Coverage   75.82%   75.80%   -0.03%     
==========================================
  Files         362      362              
  Lines      113907   113903       -4     
==========================================
- Hits        86374    86342      -32     
- Misses      27533    27561      +28     

Files with missing lines	Coverage Δ
src/LocalField/Completions.jl	96.56% <100.00%> (ø)
src/LocalField/Elem.jl	82.52% <100.00%> (ø)
src/LocalField/LocalField.jl	75.35% <100.00%> (-1.22%)	⬇️
src/LocalField/Poly.jl	63.37% <ø> (ø)
src/NumField/NfAbs/MPolyAbsFact.jl	70.25% <100.00%> (-0.51%)	⬇️
src/QuadForm/Quad/NormalForm.jl	99.55% <100.00%> (ø)
src/HeckeTypes.jl	84.36% <50.00%> (ø)
src/LocalField/Conjugates.jl	79.89% <80.00%> (+3.09%)	⬆️
src/LocalField/qAdic.jl	77.77% <0.00%> (ø)
src/Misc/UnitsModM.jl	69.26% <0.00%> (ø)
... and 3 more

... and 30 files with indirect coverage changes

[fingolfin]

Excellent!

[lgoettgens]

@thofma I think it would make sense to get this merged before doing the heavy work in Nemo that then needs #1522.

[joschmitt]

Nothing should need #1522. I think you mean #1605.

[lgoettgens]

Nothing should need #1522. I think you mean #1605.

Yes, exactly. Thanks for pointing this out.