Update localizations and schemes.

[HechtiDerLachs]

Some updates and extensions regarding the localizations and schemes.

This makes use of @thofma 's new code on polynomial maps.

[thofma]

Minor comment on a name. Since we have isisomorphic, I would suggest to change canonically_isomorphic to is[_]canonically_isomorphic.

[HechtiDerLachs]

It seems that there is a conflict with the plane curves about the definition of ProjectiveScheme. These files are still in the experimental folder.

• Who is using them?
• Is anyone still developing this? Who can I talk to about making the two patches coherent?
• If there's nobody available for the latter: How important is it that the projective spaces from the plane curves are being kept?
  CC: @wdecker

[HechtiDerLachs]

This PR is already quite big again, but it can be split in two main patches:

• the update on existing code in Oscar up to this commit
• some more extensions on glueings and projective schemes.

If desired, we could therefore split it into two PRs. Let me know if this would be better.

[thofma]

I can't say much about the scheme stuff. From the map point of view of this looks good. Did you see my comment about is[_]canonically_isomorphic?

[HechtiDerLachs]

Ok, thanks for having a look at it!

Yes, I saw your comment and I'm probably going to change it. We were not very happy with the name, anyway, so if there are any suggestions for something shorter, let me know.

BTW: I'm just running some performance tests and the hom in MPolyRing.jl, line 25, seems to be a bottleneck. Any ideas why?

[thofma]

Do you want to rename or should I just merge it as is?

[HechtiDerLachs]

Sorry, but I'm afraid, I should probably have another look at this PR. At some points (outside the MPoly(Quo)LocalizedRingHoms) I'm still using the old AlgebraHomomorphism. Should I clean this up before merging?

[thofma]

That would be great

[HechtiDerLachs]

I will rename the canonically_isomorphic routine. I also need to insert some type assertions. Sorry for not managing to do this today.

But the failing tests are not my fault, are they?

[thofma]

Yes, you can ignore them.

[HechtiDerLachs]

Just a heads up: This should be ready to be merged now. The failing checks are for other reasons.