Fixes `mres` and `nres` in `free_resolution` #3700

RafaelDavidMohr · 2024-05-07T13:56:41Z

This PR will fix the mres and nres options in free_resolution using prune_with_map. Previously, using these options
might not return a minimal free resolution.

For using prune_with_map conveniently in free_resolution, I would like add a minimal keyword to presentation, if this is set to true we would return a minimal presentation, computed from the output of prune_with_map.

@wdecker Do we want a user-facing option to compute a minimal presentation? If not, then I will do this just internally.

wdecker · 2024-05-07T16:45:09Z

@RafaelDavidMohr As far as I can see, the new functionality is only used with mres. If everybody agrees, we do not need the proposed keyword. Or?

wdecker · 2024-05-07T16:48:35Z

@jankoboehm userfacing function named minimal_presentation?

jankoboehm · 2024-05-08T08:26:57Z

Yes we want the keyword. There are use-cases for both options.

src/Modules/UngradedModules/Presentation.jl

fingolfin · 2024-05-10T12:22:03Z

src/Modules/UngradedModules/Presentation.jl

+  proj_map = hom(F0, SQ_new, gens(SQ_new), check=false)
+  F0_to_SQ = compose(proj_map, phi)
+  F0_to_SQ.generators_map_to_generators = true
+  AbstractAlgebra.set_name!(F0, "$br_name^$(ngens(SQ.sub))")


Why do you ned to set this name here and below? Since F0 and F1 are free module anyway, couldn't this be done generally as part of the show methods for free modules?

As it is, this hardcodes the name of the basering, so if it changes later on, it will look ugly. Likewise if there is no name set, you hardcode br forever.

This is the current standard for presentations/resolutions/etc. and the same at other places. Thus I would keep it like this here right now and would instead think of some way to replace all of these instances by some AA printing magic in the future.

Yeah if this is pervasive we should not try to deal with it in this PR. But perhaps we can open an issue as a reminder?

Or perhaps we just add it to #2891

RafaelDavidMohr · 2024-05-10T15:12:56Z

@wdecker @jankoboehm do you have an example where presentation produces something non-minimal that I can use as a test for the minimal free resolution?

codecov · 2024-05-10T15:44:08Z

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 81.36%. Comparing base (357c46b) to head (f2a684b).
Report is 15 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #3700      +/-   ##
==========================================
+ Coverage   81.34%   81.36%   +0.01%     
==========================================
  Files         577      577              
  Lines       78618    78674      +56     
==========================================
+ Hits        63952    64011      +59     
+ Misses      14666    14663       -3

Files	Coverage Δ
src/Modules/UngradedModules/FreeResolutions.jl	`89.53% <100.00%> (ø)`
src/Modules/UngradedModules/Presentation.jl	`69.54% <100.00%> (+5.04%)`	⬆️

... and 73 files with indirect coverage changes

wdecker · 2024-05-10T20:45:29Z

This example should do: ```julia X = rational_d9_pi6(); Pn = ambient_coordinate_ring(X) A = homogeneous_coordinate_ring(X) n = ngens(Pn)-1 c = codim(X) FA = free_resolution(A, algorithm = :fres) C = Oscar.SimpleComplexWrapper(FA.C[0:first(range(FA.C))]) C_simp = simplify(C) C_shift = shift(C_simp, c) OmegaPn = graded_free_module(Pn, [n+1]) D = hom(C_shift, OmegaPn) D_simp = simplify(D) Z, inc = kernel(D_simp, 0) B, inc_B = Oscar.boundary(D_simp, 0) M = SubquoModule(D_simp[0], ambient_representatives_generators(Z), ambient_representatives_generators(B)) ```

…

Am 10.05.2024 um 17:13 schrieb Rafael Mohr ***@***.***>: @wdecker <https://github.com/wdecker> @jankoboehm <https://github.com/jankoboehm> do you have an example where presentation produces something non-minimal that I can use as a test for the minimal free resolution? — Reply to this email directly, view it on GitHub <#3700 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AASSXETO6QBTAP236R4JSXLZBTPY7AVCNFSM6AAAAABHLCCC6KVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDCMBUG44DINJWGU>. You are receiving this because you were mentioned.

wdecker · 2024-05-10T21:26:45Z

one more: S, (x0, x1, x2, x3, x4) = graded_polynomial_ring(GF(3), ["x0", "x1", "x2", "x3", "x4"]); m = ideal(S, [x1^2+(-x1+x2+x3-x4)*x0, x1*x2+(x1-x3+x4)*x0, x1*x3+(-x1+x4+x0)*x0, x1*x4+(-x1+x3+x4-x0)*x0, x2^2+(x1-x2-x4-x0)*x0, x2*x3+(x1-x2+x3+x4-x0)*x0, x2*x4+(x1+x2-x3-x4-x0)*x0, x3^2+(x3+x4-x0)*x0,x3*x4+(-x3-x4+x0)*x0, x4^2+(x1+x3-x4-x0)*x0]); Qm, _ = quo(S, m); FQm = free_resolution(Qm) M, _ = image(map(FQm, 1))

…

Am 10.05.2024 um 17:13 schrieb Rafael Mohr ***@***.***>: @wdecker <https://github.com/wdecker> @jankoboehm <https://github.com/jankoboehm> do you have an example where presentation produces something non-minimal that I can use as a test for the minimal free resolution? — Reply to this email directly, view it on GitHub <#3700 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AASSXETO6QBTAP236R4JSXLZBTPY7AVCNFSM6AAAAABHLCCC6KVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDCMBUG44DINJWGU>. You are receiving this because you were mentioned.

RafaelDavidMohr · 2024-05-13T10:22:45Z

one more: S, (x0, x1, x2, x3, x4) = graded_polynomial_ring(GF(3), ["x0", "x1", "x2", "x3", "x4"]); m = ideal(S, [x1^2+(-x1+x2+x3-x4)x0, x1x2+(x1-x3+x4)x0, x1x3+(-x1+x4+x0)x0, x1x4+(-x1+x3+x4-x0)*x0, x2^2+(x1-x2-x4-x0)x0, x2x3+(x1-x2+x3+x4-x0)x0, x2x4+(x1+x2-x3-x4-x0)*x0, x3^2+(x3+x4-x0)x0,x3x4+(-x3-x4+x0)*x0, x4^2+(x1+x3-x4-x0)*x0]); Qm, _ = quo(S, m); FQm = free_resolution(Qm) M, _ = image(map(FQm, 1))

Do we know the correct ranks for the minimal free resolution in this example so I can test?

wdecker · 2024-05-13T13:08:36Z

In _presentation_minimal please catch border case of a free module before entering
AbstractAlgebra.set_name!(F0, "$br_name^$(ngens(SQ.sub))")

wdecker · 2024-05-14T08:48:13Z

There is a problem with the print function:

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

julia> A = R[x 1 y; 2x^2 z^2 3y^2];

julia> M = cokernel(A);

julia> PM = presentation(M)
0 <---- M <---- R^3 <---- R^2

julia> MPM = _presentation_minimal(M)
0 <---- M <---- R^3 <---- R^1

julia> matrix(map(MPM,1))
[-2x^2 + xz^2 -3y^2 + yz^2]

julia> MPM[0]
Free module of rank 2 over R

RafaelDavidMohr · 2024-05-14T09:54:24Z

In _presentation_minimal please catch border case of a free module before entering AbstractAlgebra.set_name!(F0, "$br_name^$(ngens(SQ.sub))")

This case is caught in presentation already, and the user will only access _presentation_minimal via the minimal kw of presentation. Should I nonetheless treat this case seperately?

RafaelDavidMohr · 2024-05-14T09:58:55Z

M = cokernel(A);

Fixed with f2a684b

wdecker · 2024-05-14T10:00:00Z

I am not sure what our policy here is. It may happen that a future developer may use this internal function and run into the border case. @fingolfin what do you think?

…

Am 14.05.2024 um 11:54 schrieb Rafael Mohr ***@***.***>: In _presentation_minimal please catch border case of a free module before entering AbstractAlgebra.set_name!(F0, "$br_name^$(ngens(SQ.sub))") This case is caught in presentation already, and the user will only access _presentation_minimal via the minimal kw of presentation. Should I nonetheless treat this case seperately? — Reply to this email directly, view it on GitHub <#3700 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AASSXESK2FX6YF5GPGO34LDZCHNONAVCNFSM6AAAAABHLCCC6KVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDCMBZG43TINRTGA>. You are receiving this because you were mentioned.

src/Modules/UngradedModules/Presentation.jl

fingolfin · 2024-05-15T08:11:52Z

@wdecker I am afraid I don't understand what you are asking about. What is "this internal function", and which border case?

Happy to talk about it during triage today if anyone would like to.

lgoettgens · 2024-05-15T08:19:26Z

@wdecker I am afraid I don't understand what you are asking about. What is "this internal function", and which border case?

Happy to talk about it during triage today if anyone would like to.

I think I understood the issue and can try to explain it later in triage if wdecker is not there

RafaelDavidMohr · 2024-05-16T16:36:17Z

I added the discussed minimization of the kernel in _presentation_minimal. I added it with an optional keyword, so that it can easily be integrated into free_resolution.

Currently this uses prune_with_map. I tried to use Singular.mres but this function seems to ignore the length argument.

@wdecker Should I make a Singular issue regarding this?

ederc · 2024-05-16T17:29:32Z

Can you give a concrete example where Singular.mres ignores the length argument? If I compute a free resolution with current Oscar master using algorithm = :mres and length set, it seems to compute up to the correct length.

wdecker

This is ready to go as soon as the tests are green. Please check tests.

RafaelDavidMohr · 2024-05-21T09:56:21Z

Can you give a concrete example where Singular.mres ignores the length argument? If I compute a free resolution with current Oscar master using algorithm = :mres and length set, it seems to compute up to the correct length.

Maybe I'm misunderstanding the concept of length of a free resolution, but for example

julia> R, (x, y, z) = polynomial_ring(GF(65521), ["x", "y", "z"]);

julia> I = ideal(R, [x^2, x*y, y]);

julia> M = ideal_as_module(I);

julia> sf = Oscar.singular_module(ambient_free_module(M));

julia> sm = Singular.Module(base_ring(sf), [sf(repres(g)) for g in gens(M)]...);

julia> Singular.mres(sm, 1)
Singular resolution: R^1 <- R^2 <- R^1

julia> Singular.mres(sm, 2)
Singular resolution: R^1 <- R^2 <- R^1

julia> Singular.mres(sm, 3)
Singular resolution: R^1 <- R^2 <- R^1

wdecker · 2024-05-21T10:15:12Z

@RafaelDavidMohr In your example, the resolution is short, so entering an increased length will not change anything:

julia> R, (x, y) = polynomial_ring(GF(65521), ["x", "y"]);

julia> I = ideal(R, [x^2, x*y, y]);

julia> M = ideal_as_module(I);

julia> FM = free_resolution(M, algorithm = :mres, length = 1)
Free resolution of M
R^3 <---- R^2
0 1

julia> FM = free_resolution(M, algorithm = :mres, length = 0)
Free resolution of M
R^3 <---- R^2 <---- 0
0 1 2

So why now does Singular print this:

julia> Singular.mres(sm, 1)
Singular resolution: R^1 <- R^2 <- R^1

I guess, this is due to the fact that you use mres. So you have to go one step further in order to minimalize. @hannes14 ?

* Adjusting docu following PR #3700 * More illustrative example * Documenting more methods and improving text * remove white space

fingolfin reviewed May 10, 2024

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fingolfin reviewed May 10, 2024

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RafaelDavidMohr force-pushed the rm/mres branch from 7853d61 to 3835a16 Compare May 13, 2024 10:08

lgoettgens reviewed May 14, 2024

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

lgoettgens mentioned this pull request May 15, 2024

Fix name handling of elements of complexes/presentations/resolutions #3730

Closed

Rafael Mohr added 7 commits May 16, 2024 18:09

adds _presentation_minimal

f114393

adds minimal kw to presentation

18a21c6

use minimal kw in free_resolution

8ad3ad8

if -> elseif

9f41c6a

fix printing

92198c3

minimize kernel in _presentation_minimal

74ef0ae

min presentation test

de04160

RafaelDavidMohr force-pushed the rm/mres branch from f2a684b to de04160 Compare May 16, 2024 16:33

wdecker approved these changes May 17, 2024

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fix tests

5cef808

fix tests

f0641a2

ederc marked this pull request as ready for review May 22, 2024 10:21

ederc merged commit d9d6bae into oscar-system:master May 22, 2024
26 checks passed

wdecker added a commit that referenced this pull request May 24, 2024

Adjusting docu following PR #3700

d6b2392

jankoboehm pushed a commit that referenced this pull request May 29, 2024

Adjusting docu following PR #3700 (#3795)

ff7aed4

* Adjusting docu following PR #3700 * More illustrative example * Documenting more methods and improving text * remove white space

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Fixes `mres` and `nres` in `free_resolution` #3700

Fixes `mres` and `nres` in `free_resolution` #3700

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Fixes mres and nres in free_resolution #3700

Fixes mres and nres in free_resolution #3700

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Fixes `mres` and `nres` in `free_resolution` #3700

Fixes `mres` and `nres` in `free_resolution` #3700

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