Module quotients I

[wdecker]

No description provided.

[fingolfin]

Just FYI these days you could also write

Suggested change

	julia> R, (x, y, z) = polynomial_ring(QQ, [:x, :y, :z]);
	julia> R = @polynomial_ring(QQ, [:x, :y, :z]);

[wdecker]

Thx, the next time ...

[codecov]

Codecov Report

Attention: Patch coverage is 96.15385% with 1 line in your changes missing coverage. Please review.

Project coverage is 84.60%. Comparing base (8451da1) to head (a83ef7d).
Report is 6 commits behind head on master.

Files with missing lines	Patch %	Lines
src/Modules/UngradedModules/SubquoModule.jl	96.15%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #4217   +/-   ##
=======================================
  Coverage   84.60%   84.60%           
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  Files         631      631           
  Lines       84915    84954   +39     
=======================================
+ Hits        71842    71878   +36     
- Misses      13073    13076    +3     

Files with missing lines	Coverage Δ
experimental/Schemes/src/ProjectiveModules.jl	83.24% <ø> (-0.92%)	⬇️
src/Modules/UngradedModules/SubquoModule.jl	77.41% <96.15%> (+1.88%)	⬆️

... and 4 files with indirect coverage changes

[wdecker]

@thofma The failing test here signals a problem in number theory. Any idea?

[thofma]

Yes, this is #4170 can be ignored.

[wdecker]

@HechtiDerLachs Can you please check whether you agree and if so, merge this PR. In the next PR I wish to do quotients of type M:J, M module, J ideal. Do you have already a generic method for this? Can we reasonably reduce this to annihilator?

[HechtiDerLachs]

In the next PR I wish to do quotients of type M:J, M module, J ideal. Do you have already a generic method for this?

No, I don't think I or anyone else has implemented a generic method for this, yet.

Can we reasonably reduce this to annihilator?

I don't see this straight away. There are certainly generic implementations of this. But already my implementation for annihilator was probably not the most effective one. I just wanted to have something working at the time. Maybe it's best to implement this as a kernel of an appropriate map M \to (F/M)^k where M \subset F is a submodule of a free module, k is the number of generators of J and the j-th component of the map is multiplication with that generator?

As you said the other day, we should wrap the established Singular routine for the polynomial case.