Add dev docs on caching parent objects

[fingolfin]

Following the discussions last Friday and again this Wednesday, where Claus explained the caching rules as they were so far; I've now tried to codify them here, for future reference or revision. In particular, what I describe here is not meant to be something new, but reflect what was the policy so far.

I am sure I forgot stuff or maybe even misrepresented something, so please let the feedback flow in.

Resolves #3616

[fingolfin]

I just discovered some notes on caching at https://nemocas.github.io/AbstractAlgebra.jl/dev/ring_interface/#Parent-object-caches -- perhaps some of that should also be included or referenced here (and/or perhaps the text there should be updated). I'll wait to hear what @fieker thinks.

[joschmitt]

Funnily enough, exactly this example doesn't work because caching is deliberately turned off:

julia> M = QQ[1 0; 0 1];

julia> charpoly(M)*charpoly(M)
ERROR: Incompatible polynomial rings in polynomial operation
[...]

[fingolfin]

Ouch! Thank you very much for fact checking this.

That makes me question the point of entire caching thing even more sigh.

So, does anyone then have a not completely unconvincing example for a situation where a cached parent helps a "naive" user?

[joschmitt]

Tommy also mentioned issues with parallelization/thread safety as a (possible) downside to me.

(And I don't really understand how the memory could fill up if we use these WeakValueDicts? But that's more for my curiosity.)

[fingolfin]

Unfortunately not all our caches actually use WeakValueDict. We introduced it much later and e.g. Hecke still uses Dict and IdDict caches quite a bit (I just grepped for get_cached! to find examples for caches and then checked their definitions). Might be a good idea for somebody to clean that up.

[joschmitt]

I hope that I got all caching dictionaries which weren't WeakValueDicts in Nemocas/Nemo.jl#1724 and thofma/Hecke.jl#1460.

[joschmitt]

This matches what I was told over the past years. It's good to have a 'reference' now.

[fieker]

Maybe add Hecke.clear_cache() which tries its best to empty all(?) caches in AA, Nemo and Hecke?

[thofma]

julia> Zx, x = ZZ["x"]
(Univariate polynomial ring in x over ZZ, x)

julia> F = GF(2);

julia> map_coefficients(F, x^2) + map_coefficients(F, x)
x^2 + x

[fieker]

it moves into the right direction.

[fingolfin]

Thanks @thofma I've added your nice example.

BTW I find it quite disheartening that I get this on my M1 MacBook the first time I execute map_entries (that's not direct against Tommy or against anyone, really, just something that makes me sad / where we badly need to improve, somehow)

julia> Zx, x = ZZ["x"]
(Univariate polynomial ring in x over ZZ, x)

julia> F = GF(2);

julia> @time map_coefficients(F, x^2);
 11.979656 seconds (60.42 M allocations: 3.764 GiB, 7.85% gc time, 100.00% compilation time)

julia> @time map_coefficients(F, x^2);
  0.000021 seconds (18 allocations: 976 bytes)