Update argument order in compose

[lgoettgens]

This updates all definitions and uses of compose in Nemo according to oscar-system/Oscar.jl#690 to follow compose(f,g) = g(f(x)).

This change is obviously breaking.

[lgoettgens]

Cf. the discussion in Nemocas/AbstractAlgebra.jl#1025

[codecov]

Codecov Report

Merging #1521 (0a29061) into master (38fd074) will increase coverage by 0.65%.
Report is 6 commits behind head on master.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master    #1521      +/-   ##
==========================================
+ Coverage   82.75%   83.40%   +0.65%     
==========================================
  Files          95       95              
  Lines       37186    39032    +1846     
==========================================
+ Hits        30773    32556    +1783     
- Misses       6413     6476      +63     

Files Changed	Coverage Δ
src/arb/ComplexPoly.jl	79.53% <ø> (ø)
src/arb/RealPoly.jl	79.35% <ø> (ø)
src/arb/acb_poly.jl	77.23% <ø> (ø)
src/arb/arb_poly.jl	78.38% <ø> (ø)
src/flint/fmpq_poly.jl	94.93% <ø> (+0.31%)	⬆️
src/flint/fmpz_mod_poly.jl	94.86% <ø> (ø)
src/flint/fq_default_poly.jl	93.50% <ø> (ø)
src/flint/fq_nmod_poly.jl	93.02% <ø> (ø)
src/flint/fq_poly.jl	97.04% <ø> (ø)
src/flint/nmod_poly.jl	90.02% <ø> (ø)
... and 2 more

... and 15 files with indirect coverage changes

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[fingolfin]

The breakage this introduces is of a worse kind than other such PRs, because instead of causing compile errors, it may result in some code actually continuing to work but return wrong results. I have no brilliant solution for this, though, other than perhaps it would be good to add compose_left and compose_right (but then who can remember which is which); or precompose / postcompose (but again I am not sure if people can remember; plus these are harder to find for tab completion). Hrm.

If we had compose_left / compose_right (or whatever), then code could be converted to use them, making remaining uses of compose stand out more. Then we could rip off the bandaid in two steps: in one we disable compose completely for a release (to catch any remaining code using it), and then in a later release could add it back...

(Personally I think what I could work with best myself is to use * and $\circ$ operators: I have been drilled since high school that $(f\circ g)(x) = f(g(x))$, and later learned that $x^{fg}=x^{f\cdot g} = x^{fg} = (x^f)^g$, i.e., $(fg)(x) = g(f(x))$. However, besides the obvious issue due to use of unicode, I also suspect that many won't be familiar with one or both of these, too.

Hrm. Sorry, no great solution from me here. We should still resolve this eventually, somehow!

[thofma]

Could we perhaps keep the discussion at oscar-system/Oscar.jl#690?

[lgoettgens]

Making this a draft to prevent accidental merge

[lgoettgens]

too many conflicts. closing