addresseing Issue #2427

[wdecker]

No description provided.

[fingolfin]

This PR looks good to me, with the caveat that I have no idea what the change in the schemes code from isprime(D) to isone(D) || isprime(D) does and if it is the right thing to do.

[HechtiDerLachs]

Let's see whether this works.

[codecov]

Codecov Report

Merging #2473 (e90d80e) into master (cf57c0f) will decrease coverage by 0.02%.
The diff coverage is 84.61%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2473      +/-   ##
==========================================
- Coverage   73.12%   73.11%   -0.02%     
==========================================
  Files         400      400              
  Lines       53588    53607      +19     
==========================================
+ Hits        39188    39194       +6     
- Misses      14400    14413      +13     

Impacted Files	Coverage Δ
src/Rings/mpoly-ideals.jl	84.34% <80.00%> (-0.56%)	⬇️
experimental/Schemes/IdealSheaves.jl	82.75% <100.00%> (+0.21%)	⬆️

... and 9 files with indirect coverage changes

[simonbrandhorst]

Looks good to me. Somewhat aside to this PR:

I think that is_prime(::IdealSheaf) does not do what it is supposed to. We only check that it is locally prime at some open cover. But I would say that is not a local property. Because we can take a disconnected scheme of two points {P1,P2} and take the open cover U1 = {P1} and U2={P2}. Now consider the zero sheaf of ideals.
It will be locally prime but not globally.
So what our function checks is just that a sheaf of prime ideals is locally prime. But we do not check that it is prime for every affine open (e.g. the affine open containing both {P1,P2}). And even if we could, I am not sure if we still get something irreducible in the non-separated case.

In any case this behavior is unrelated to the PR and we should discuss it in an issue.

[afkafkafk13]

Looks good to me. Somewhat aside to this PR:

I think that is_prime(::IdealSheaf) does not do what it is supposed to. We only check that it is locally prime at some open cover. But I would say that is not a local property. Because we can take a disconnected scheme of two points {P1,P2} and take the open cover U1 = {P1} and U2={P2}. Now consider the zero sheaf of ideals. It will be locally prime but not globally. So what our function checks is just that a sheaf of prime ideals is locally prime. But we do not check that it is prime for every affine open (e.g. the affine open containing both {P1,P2}). And even if we could, I am not sure if we still get something irreducible in the non-separated case.

In any case this behavior is unrelated to the PR and we should discuss it in an issue.

I agree and would like to add that is_connected is not yet implemented for schemes, whence the above issue is not one to be fixed within days.