Faster computation of injective resolutions

[annahofer00]

This PR improves the speed of computing injective resolutions significantly. The improvement comes from computing the irreducible resolution only up to the required cohomological degree.

[annahofer00]

Hi everyone,

it seems like something goes wrong that has nothing to do with my changes. When constructing a quotient by some submodule, elements in the submodule (sometimes?) have no preimage, which is weird. Can someone look into this? The error occurs for example in the test-set 'local_cohomology_first_example.jl'.

Thanks!
Anna

[lgoettgens]

Hi everyone,

it seems like something goes wrong that has nothing to do with my changes. When constructing a quotient by some submodule, elements in the submodule (sometimes?) have no preimage, which is weird. Can someone look into this? The error occurs for example in the test-set 'local_cohomology_first_example.jl'.

Thanks! Anna

This looks like something @HechtiDerLachs or @jankoboehm could help with.

[HechtiDerLachs]

This looks like something @HechtiDerLachs or @jankoboehm could help with.

Indeed, this should be the same problem as whitnessed on #5490. But unfortunately here we do not have the possibility to use such a simple workaround. We have deliberately decided to use the SubModuleOfFreeModule-layer over quotient rings directly here.

I can look into fixing this temporarily, too. But I think it would be best if the problem could be solved in Singular directly.

[HechtiDerLachs]

I tried locally to rebase this on #5492 to see whether the problem here goes away. But it doesn't.

Looking at the issue here a bit more closely, I'm wondering whether this is actually related to #5490 . The error occurs somewhere in code which is using the modules over fields from AA, not the commutative algebra modules from Oscar. Moreover, it appears that you are trying to compute some homology H = Z/B, but in your case B is not a subset of Z. Did you check that the incoming and outgoing map actually compose to zero?

As an outsider it is a bit difficult for me to see where everything is coming from here. Do the incoming and outgoing map arise from some saturation? If yes, we can look into fixing this. If not, then I suggest you first have a look into this issue yourself again.

[HechtiDerLachs]

@annahofer00 : I was trying to reach out to you on Slack. Not sure that came through, though. Either way: Let me know if there are questions on how to proceed with this.

[lgoettgens]

I am not familiar with the mathematics at all, thus pinged two other people that know some stuff about commutative algebra, and worked with this code before