Add `mres` and `nres` Singular Calls for Free resolutions #2500

RafaelDavidMohr · 2023-06-29T11:59:54Z

Adds corresponding keywords to free_resolution and adjusts docu accordingly.

src/Modules/UngradedModules.jl

wdecker · 2023-06-29T12:34:21Z

src/Modules/UngradedModules.jl

  elseif algorithm == :sres
    res = Singular.fres(singular_kernel_entry, length)


There seems to be an old bug: you want sres but ask for fres!

Fixed in d6abd9f

wdecker · 2023-06-29T12:36:04Z

Once this is merged, I will extend the docu and explain what the difference between the different methods is.

fingolfin · 2023-06-29T13:19:22Z

Project.toml

@@ -35,7 +35,7 @@ Polymake = "0.10.0"
 Preferences = "1"
 RandomExtensions = "0.4.3"
 RecipesBase = "1.2.1"
-Singular = "0.18.2"
+Singular = "0.18.6"


This looks right (I didn't check the versions, but I trust you did).

Thanks!

fingolfin · 2023-06-29T13:21:02Z

This PR has no test for the new code, so naturally it will pass, even if actually calling the code was broken.

So either a test should be added in this PR (could be a doctest or could be a regular test); or else I'd hope that @wdecker would add one when he extends the documentation for this?

RafaelDavidMohr · 2023-06-29T15:17:27Z

A word on the now failing tests: I could be wrong, but to me it seems that the issue is the following:

Oscar starts computing a free resolution by computing the input module as a cokernel and then passes that cokernel to Singular to let it compute a free resolution for that. Singular.sres returns this free resolution but with the generators of this cokernel potentially permuted. Now the presentation of the input module and the Singular resolution don't "patch together" correctly and thus give a wrong free resolution in Oscar.

My question is: Should we try to handle this bug in this PR or a seperate one?

wdecker

There are several problems here: To begin with, fres and sres require as input a gröbner basis. This is missing so far. There is another problem on which @jankoboehm is already working.

For the time being, I suggest to replace sres by fres in the test. If this makes the test pass, let us merge the PR. More tests and docu will be added as soon as all problems are fixed. @RafaelDavidMohr please open an issue which reminds us to do the above.

RafaelDavidMohr · 2023-06-30T08:01:53Z

Unfortunately the same problem seems to be happening with mres: Singular changes the cokernel representation of the module and then the free resolution Singular gives doesn't glue correctly with what is computed on the Oscar side.

So mres would require similar changes to the free resolution code that sres needs.

wdecker · 2023-06-30T09:51:21Z

The situation for mres is different and more subtle as mres computes a new presentation. In particular, this requires that we return an isomorphism between the given module and the new module. That means that we have to introduce some book-keeping in Singular and add the result of this to the output of mres. So let me suggest to make this PR a draft until all these prblems have been addressed.

RafaelDavidMohr · 2023-06-30T10:18:36Z

The situation for mres is different and more subtle as mres computes a new presentation. In particular, this requires that we return an isomorphism between the given module and the new module. That means that we have to introduce some book-keeping in Singular and add the result of this to the output of mres. So let me suggest to make this PR a draft until all these prblems have been addressed.

Ok! In a sence, sres also computes a new representation (but just by shuffling around generators).

Let me know if I can help with fixing this.

fingolfin · 2023-08-23T10:13:58Z

We think there are some changes in the latest Singular.jl that may help, but couldn't find them just now; but @hannes14 will check

RafaelDavidMohr · 2023-09-07T09:19:51Z

I added mres, the bug that I originally described (with Singular changing the presentation of some module) looks to be actually easily fixed by some global changes to the free_resolution function, we just have to also take the first map that Singular gives us.

Let me know if I missed something.

ederc · 2023-09-07T11:21:37Z

Looks like a valid solution to me.

test/Modules/UngradedModules.jl

fingolfin · 2023-09-11T09:49:03Z

If the geometry would like to merge this, fine by me, but someone needs to explicitly approve it

wdecker · 2023-09-11T09:51:24Z

We are still discussing it. Will be merged tomorrow.

…

Am 11.09.2023 um 11:49 schrieb Max Horn ***@***.***>: If the geometry would like to merge this, fine by me, but someone needs to explicitly approve it — Reply to this email directly, view it on GitHub <#2500 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AASSXEXBII5IO7TWHQP2DP3XZ3NBXANCNFSM6AAAAAAZYNCDTQ>. You are receiving this because you were mentioned.

codecov · 2023-09-11T12:08:09Z

Codecov Report

Merging #2500 (347349c) into master (79874fd) will increase coverage by 0.72%.
Report is 24 commits behind head on master.
The diff coverage is 74.80%.

@@            Coverage Diff             @@
##           master    #2500      +/-   ##
==========================================
+ Coverage   73.63%   74.36%   +0.72%     
==========================================
  Files         455      455              
  Lines       64411    68587    +4176     
==========================================
+ Hits        47427    51002    +3575     
- Misses      16984    17585     +601

Files Changed	Coverage
experimental/JuLie/src/schur_polynomials.jl	`ø`
...ntal/QuadFormAndIsom/src/lattices_with_isometry.jl	`ø`
experimental/Schemes/CoveredProjectiveSchemes.jl	`ø`
src/AlgebraicGeometry/Schemes/Glueing/Methods.jl	`ø`
...eometry/Schemes/ProjectiveSchemes/Objects/Types.jl	`ø`
src/Modules/FreeModules-graded.jl	`0.00%`
src/Rings/mpoly-affine-algebras.jl	`0.00%`
src/Rings/mpoly-graded.jl	`0.00%`
src/TropicalGeometry/curve.jl	`0.00%`
src/Serialization/containers.jl	`20.00%`
... and 13 more

RafaelDavidMohr · 2023-09-12T08:59:33Z

Here is a bit more explanation on why things should work now. Originally I diagnosed the problem wrong.

Previously, for a given module M, free_resolution(M) would perform the following computations:

We start by computing a presentation of M

0 <-- M <-- F <-- G

then we let C be the cokernel of this representation (i.e. the image of G in F) and let Singular compute a free resolution of this cokernel:

0 <-- F/C <-- F0 <-- F1 <-- F2 <-- ...

and now the two chain complexes were patched together as follows:

0 <-- M <-- F <-- G <-- F2 <-- ...

F and F0 are always the same, but the problematic part is F <-- G <-- F2 because the image of G in F (==F0) might have its generators sorted differently or altogether changed compared to the image of F1 in F0. Then the homology is nonzero at G. This is now fixed by instead returning

0 <-- M <-- F <-- F1 <-- F2 <-- ...

This is now always a correct free resolution (because we basically just take the one Singular gives us, F = F0 is always guaranteed). I hope this helps.

wdecker · 2023-09-12T15:09:23Z

@RafaelDavidMohr Thx for doing this.

I have a small remark: The methods

free_resolution(I::MPolyIdeal)

free_resolution(Q::MPolyQuoRing)

and also the "dummy" method

free_resolution(F::FreeMod)

should be adjusted to the syntax we have now for free_resolution.

jankoboehm · 2023-09-13T06:31:18Z

As I understand it, we switch the presentation matrix originally computed by OSCAR to the (in case of mres, not fres) possibly modified one returned by Singular. Are we sure that this is the same module and not just an isomorphic one (then we have to keep track of the isomorphism), what if we resolve a submodule. We cannot change the generators, since the representation of the elements is referencing them. It also looks to me as if the grading is removed? Best have a quick talk in person once possible.

RafaelDavidMohr · 2023-09-13T09:26:56Z

As I understand it, we switch the presentation matrix originally computed by OSCAR to the (in case of mres, not fres) possibly modified one returned by Singular. Are we sure that this is the same module and not just an isomorphic one (then we have to keep track of the isomorphism), what if we resolve a submodule. We cannot change the generators, since the representation of the elements is referencing them. It also looks to me as if the grading is removed? Best have a quick talk in person once possible.

Yes, in person (Saarbrücken for instance) is probably easier. I will however have a look at the grading issue and at the things @wdecker mentioned.

Edit: Actually, @jankoboehm, I am not sure what you mean by "the grading is removed". I tried a random example and I'm getting a graded free resolution. Could you specify?

RafaelDavidMohr · 2023-09-13T10:01:59Z

@RafaelDavidMohr Thx for doing this.

I have a small remark: The methods

free_resolution(I::MPolyIdeal)

free_resolution(Q::MPolyQuoRing)

and also the "dummy" method

free_resolution(F::FreeMod)

should be adjusted to the syntax we have now for free_resolution.

See 347349c. I adjusted the docu accordingly, the docu for free_resolution(F::FreeMod) is not ideal, let me know if I should change it.

wdecker · 2023-09-18T08:13:03Z

This is good for now. However, for the mres part, we also need to minimize the presentation we work with. This requires some work in Singular first. We will fix this asap.

* add `mres` with fix * fixes no relation edge case * adds `nres`, updated doc, adds tests * fix typo `mres` -> `nres` * compatibility changes to other `free_resolution` methods --------- Co-authored-by: Rafael Mohr <[email protected]> Co-authored-by: ederc <[email protected]>

fingolfin reviewed Jun 29, 2023

View reviewed changes

src/Modules/UngradedModules.jl Outdated Show resolved Hide resolved

wdecker reviewed Jun 29, 2023

View reviewed changes

fingolfin reviewed Jun 29, 2023

View reviewed changes

wdecker reviewed Jun 29, 2023

View reviewed changes

RafaelDavidMohr marked this pull request as draft June 30, 2023 10:19

RafaelDavidMohr force-pushed the rm/minimal-free-res branch from d6abd9f to b749b80 Compare September 7, 2023 09:17

RafaelDavidMohr marked this pull request as ready for review September 8, 2023 09:10

lgoettgens reviewed Sep 9, 2023

View reviewed changes

test/Modules/UngradedModules.jl Show resolved Hide resolved

wdecker mentioned this pull request Sep 12, 2023

Minimal free resolutions and simplify function for modules #2791

Open

wdecker mentioned this pull request Sep 13, 2023

Printing of Betti Tables #2793

Closed

RafaelDavidMohr force-pushed the rm/minimal-free-res branch from 16b8250 to 87d2059 Compare September 13, 2023 09:39

RafaelDavidMohr and others added 3 commits September 13, 2023 11:41

add mres with fix

5c04f88

fixes no relation edge case

fdff1c7

adds nres, updated doc, adds tests

c9c0d6c

fix typo mres -> nres

87d2059

compatibility changes to other free_resolution methods

347349c

wdecker approved these changes Sep 18, 2023

View reviewed changes

wdecker enabled auto-merge (squash) September 18, 2023 08:13

wdecker closed this Sep 18, 2023

auto-merge was automatically disabled September 18, 2023 08:16
Pull request was closed

wdecker reopened this Sep 18, 2023

wdecker merged commit b0569e7 into oscar-system:master Sep 18, 2023

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

Add `mres` and `nres` Singular Calls for Free resolutions #2500

Add `mres` and `nres` Singular Calls for Free resolutions #2500

RafaelDavidMohr commented Jun 29, 2023

wdecker Jun 29, 2023

RafaelDavidMohr Jun 29, 2023

wdecker commented Jun 29, 2023

fingolfin Jun 29, 2023

fingolfin commented Jun 29, 2023

RafaelDavidMohr commented Jun 29, 2023

wdecker left a comment

RafaelDavidMohr commented Jun 30, 2023

wdecker commented Jun 30, 2023

RafaelDavidMohr commented Jun 30, 2023

fingolfin commented Aug 23, 2023

RafaelDavidMohr commented Sep 7, 2023

ederc commented Sep 7, 2023

fingolfin commented Sep 11, 2023

wdecker commented Sep 11, 2023 via email

codecov bot commented Sep 11, 2023 •

edited

Loading

RafaelDavidMohr commented Sep 12, 2023 •

edited

Loading

wdecker commented Sep 12, 2023

jankoboehm commented Sep 13, 2023

RafaelDavidMohr commented Sep 13, 2023 •

edited

Loading

RafaelDavidMohr commented Sep 13, 2023

wdecker commented Sep 18, 2023

		elseif algorithm == :sres
		res = Singular.fres(singular_kernel_entry, length)

Add mres and nres Singular Calls for Free resolutions #2500

Add mres and nres Singular Calls for Free resolutions #2500

Conversation

RafaelDavidMohr commented Jun 29, 2023

wdecker Jun 29, 2023

Choose a reason for hiding this comment

RafaelDavidMohr Jun 29, 2023

Choose a reason for hiding this comment

wdecker commented Jun 29, 2023

fingolfin Jun 29, 2023

Choose a reason for hiding this comment

fingolfin commented Jun 29, 2023

RafaelDavidMohr commented Jun 29, 2023

wdecker left a comment

Choose a reason for hiding this comment

RafaelDavidMohr commented Jun 30, 2023

wdecker commented Jun 30, 2023

RafaelDavidMohr commented Jun 30, 2023

fingolfin commented Aug 23, 2023

RafaelDavidMohr commented Sep 7, 2023

ederc commented Sep 7, 2023

fingolfin commented Sep 11, 2023

wdecker commented Sep 11, 2023 via email

codecov bot commented Sep 11, 2023 • edited Loading

Codecov Report

RafaelDavidMohr commented Sep 12, 2023 • edited Loading

wdecker commented Sep 12, 2023

jankoboehm commented Sep 13, 2023

RafaelDavidMohr commented Sep 13, 2023 • edited Loading

RafaelDavidMohr commented Sep 13, 2023

wdecker commented Sep 18, 2023

Add `mres` and `nres` Singular Calls for Free resolutions #2500

Add `mres` and `nres` Singular Calls for Free resolutions #2500

codecov bot commented Sep 11, 2023 •

edited

Loading

RafaelDavidMohr commented Sep 12, 2023 •

edited

Loading

RafaelDavidMohr commented Sep 13, 2023 •

edited

Loading