Recog An/Sn unknown degree: conder, holt by ssiccha · Pull Request #265 · gap-packages/recog

ssiccha · 2021-04-09T15:25:27Z

A PR based on #176.

We are going to implement the extensions by Conder and Derek Holt's
GuessAltSymDegree.

ssiccha · 2021-04-12T12:12:12Z

Rebased the last commit onto the current version of #176.

codecov · 2021-04-12T12:21:57Z

Codecov Report

❌ Patch coverage is 75.32468% with 95 lines in your changes missing coverage. Please review.
✅ Project coverage is 70.48%. Comparing base (c309d8a) to head (16bace0).

Files with missing lines	Patch %	Lines
gap/generic/SnAnUnknownDegree.gi	75.13%	95 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #265      +/-   ##
==========================================
+ Coverage   69.12%   70.48%   +1.35%     
==========================================
  Files          43       43              
  Lines       18321    18637     +316     
==========================================
+ Hits        12665    13136     +471     
+ Misses       5656     5501     -155

Files with missing lines	Coverage Δ
gap/matrix.gi	`92.97% <100.00%> (+0.01%)`	⬆️
gap/perm.gi	`79.76% <100.00%> (+0.07%)`	⬆️
gap/projective.gi	`83.17% <100.00%> (+0.08%)`	⬆️
gap/generic/SnAnUnknownDegree.gi	`85.07% <75.13%> (-5.02%)`	⬇️

... and 12 files with indirect coverage changes

🚀 New features to boost your workflow:

❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

FriedrichRober · 2022-03-28T19:53:53Z

Link to our Hackmd

ssiccha · 2022-03-29T23:35:23Z

We should be almost done. We think there are two TODOs left: clean up the tests and figure out what to do with small classical groups like: Omega(-1,4,3). It has element orders <= 5, thus slips through our heuristics to weed out groups which are not isomorphic to An or Sn. Hence the SnAnUnknownDegree algorithm takes forever until it realizes, that the group in question is not an An or Sn. We think we should be able to alleviate this by simply saying that we're NeverApplicable if the vector space our group acts has less than e.g. 100 elements. And then we'll post a challenge on slack or the GAP forum whether somebody can find a small group, which makes the algorithm run slow.

And get the tests to pass again. :)

And in Make CallMethods directly write into the RecogNode update the docs of CallMethods.

And, @FriedrichRober is writing a short text, how all the parts fit together, that is how our implementation differs from a "vanilla" implementation of the JLNP algorithm according to the paper.

fingolfin · 2022-03-30T13:45:31Z

Awesome, thank you!

fingolfin · 2022-04-06T22:29:37Z

@FriedrichRober do you think you can finish this on your own, now that @ssiccha is gone? Perhaps I can help a bit?

FriedrichRober · 2022-04-07T06:47:22Z

Yes, I think I can finish this on my own. The code is finished (except for handling small classical groups). What is missing now is to finish the documentation (comments) and looking at the runtime of the test suite.

FriedrichRober · 2022-11-07T03:42:42Z

@fingolfin, ich habe nun die Änderungen implementiert, wie wir es besprochen haben. Wir geben früher auf, und speichern uns die Iteratoren im recog node ab, um sie später weiter zu verwenden. Trotzdem dauert die Test-Suite auf meinem Rechner 3-4 Minuten länger als auf dem master. Meiner Meinung nach ist dieser Zustand inakzeptabel, um das einfach so zu mergen :(

Ich muss dann nochmal genau schauen, an welchen Stellen wir zu viel Zeit verschwenden, und ob sich da was machen lässt.

TWiedemann · 2026-03-24T10:20:01Z

I am finished with my review. Everything looks good, so I think we can merge as seen as all comments above are resolved.

I think this PR will resolve #348, but correct me if I am wrong.

fingolfin · 2026-05-12T08:55:48Z

+# - slpToStdGens: an SLP from the generators of G to stdGens.
 RECOG.ConstructSnAnIsomorphism := function(ri, n, stdGensAnWithMemory)
-    local stdGensAn, xis, gImage, foundOddPermutation, slp, eval,
+    local stdGensAn, filter, filterPart, gImage, foundOddPermutation, slp, eval,


Why is this called filter? It is neither a filter in GAP's sense, nor in the mathematical sense (think "ultrafilter") nor do any of the sources use this term. I find it rather confusing.

If I remember correctly, we used the word "filter" because the xis act like a sieve or filtering mechanism on the search space for finding the image points. But any renaming would be fine here :)

fingolfin · 2026-05-12T09:03:58Z

+    # Construct filter. In <Cite Key="C12"/> filter is called E.
+    # In <Cite Key="JLNP13"/> filter is called `xi`.


It would be better if we had more concrete refs (so to specific definitions/lemmas); as it is we could not quite tell which "xi" or "Xi" or "X_i" or "x_i" are meant exactly.

I also note that RECOG.ConstructXiAn comes from the older code written for the paper by Beals et all (BLN+03 here?), so perhaps that is also a reference?

(Of course the fact that RECOG.ConstructXiAn in turn is undocumented doesn't help either...)

Yes, this is indeed from BLN+03. It is introduced in prose, so has no reference, and then is used for the first time in Lemma 5.3. If n>=11, then this filter can be used to find the image under the homomorphism. For degree <11, we had to use Conder's algorithm for the image computation, which works for degree>=5.

Co-authored-by: Torben Wiedemann <7226617+TWiedemann@users.noreply.github.com> Co-authored-by: Max Horn <max@quendi.de>

fingolfin · 2026-05-12T15:18:28Z

+##  ----------------
+##
+##  Here we describe the general strategy that is used to recognise if a group
+##  is ismorphic to `An` or `Sn` for `n >= 7`.


But below when defining SnAnUnknownDegree (around line 1355ff), it is stated that this method is for $n\geq 9$. Some parts of the code suggest that certain operations require $n\geq 9$ and others $n\geq 7$, which might explain the difference (and of course it would mean overall we indeed need $n\geq 9$).

And then there is the code in RECOG.SnAnUpperBoundForDegree which kinda seems to suggest we might have to assume $n\geq 10$, at least for non-projective matrix groups?!

Let me check this quickly so you don’t end up on a wild goose chase.

I think we can recognise groups with degree n>=7, and that groups with degree 5 or 6 cannot be recognised.

Details:

Lower Bounds need n >= 9:
This is just to satisfy the error-probabilities, and has no impact on the correctness of the algorithm.

Bolstering Elements are only defined for n >= 7:
This is the crucial point, which I think would lead to the algorithm returning fail for smaller degrees.

In SnAnUpperBoundForDegree:

For the projective groups, the relevant bounds are only defined for n≥9. To handle all cases, we set N:=max(8,d+2). When the actual degree is at least 9, we use the corresponding bound; otherwise, we assume the worst case, namely degree at most 8. Hence, the argument remains valid for all degrees.

Same holds for non-projective matrix groups with n>=10.

fingolfin · 2026-05-12T15:19:27Z

+##
+##  We have to be careful what we do for small degrees.
+##  If we pass an `A5`, `S5`, `A6`, `S6` into `SnAnUnknownDegree`, then it will not recognize it.
+##  If the input acts on a space with a large dimension, then this can take forever.


Is that last bit still the case? If so, a concrete example would be good so we can better guard against it (i.e., an example could be used in a test that verifies that whatever "guards" we use are effective)

I think it will not anymore run forever, since I adjusted the code to return fail more quickly. But I agree that a test case would be nice to confirm this, see my comment about bolstering elements only being defined for n>=7.

Anyway, I also think that the SnAnUnknownDegree code assumes that the input is irreducible (because it runs after FindHomMethodsProjective.NotAbsolutelyIrred in the recog framework, etc.), so these examples that Sergio and I thought of as problematic should not be passed as input to SnAnUnknownDegree at this stage.

fingolfin · 2026-05-12T15:19:59Z

+##  If we pass an `A5`, `S5`, `A6`, `S6` into `SnAnUnknownDegree`, then it will not recognize it.
+##  If the input acts on a space with a large dimension, then this can take forever.
+##
+##  - We assume that our input group `G` is a projective irreducible matrix group.


Ah, OK. That might partially address my concern from above about RECOG.SnAnUpperBoundForDegree requiring $n\geq 10$ in the non-projective case.

fingolfin · 2026-05-12T15:34:13Z

-# FindHomMethodsGeneric.SnAnUnknownDegree
-# Sn
-gap> for d in [11 .. 30] do
-> sets := Combinations([1 .. d], 2);;
-> SdOn2Sets := Action(SymmetricGroup(d), sets, OnSets);;
-> ri := RecogNode(SdOn2Sets);;
-> success := FindHomMethodsGeneric.SnAnUnknownDegree(ri);
-> if not success or not Size(ri) = Factorial(d) then
->   Print("wrong result! degree ", d, "\n");
-> fi;
-> od;
-
-# An
-gap> for d in [11 .. 30] do
-> sets := Combinations([1 .. d], 2);;
-> SdOn2Sets := Action(AlternatingGroup(d), sets, OnSets);;
-> ri := RecogNode(SdOn2Sets);;
-> success := FindHomMethodsGeneric.SnAnUnknownDegree(ri);
-> if not success or not Size(ri) = Factorial(d)/2 then
->   Print("wrong result! degree ", d, "\n");
-> fi;
-> od;


Removing this will result in quite a loss of coverage. Why do we do it?

Co-authored-by: Torben Wiedemann <7226617+TWiedemann@users.noreply.github.com>

Co-authored-by: Torben Wiedemann <7226617+TWiedemann@users.noreply.github.com> Co-authored-by: Martin Wagner <martin.wagner.dev@gmail.com>

ssiccha marked this pull request as draft April 9, 2021 15:26

ssiccha mentioned this pull request Apr 12, 2021

Implement "recognize An/Sn of unknown degree" algorithm by Jambor et al. #176

Merged

ssiccha force-pushed the frss/AnSnRecogUnknownDegree-2 branch from 5ae5367 to d40a988 Compare April 12, 2021 12:11

ssiccha force-pushed the frss/AnSnRecogUnknownDegree-2 branch from d40a988 to dc4a895 Compare April 12, 2021 12:32

FriedrichRober force-pushed the frss/AnSnRecogUnknownDegree-2 branch from dc4a895 to f162f36 Compare June 23, 2021 14:20

ssiccha force-pushed the frss/AnSnRecogUnknownDegree-2 branch from cca25fd to 35a39de Compare June 23, 2021 16:37

ssiccha mentioned this pull request Oct 5, 2021

Wrong size for finite deleted permutation module #296

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ssiccha force-pushed the frss/AnSnRecogUnknownDegree-2 branch from 96f9a25 to 705504c Compare March 28, 2022 22:01

FriedrichRober force-pushed the frss/AnSnRecogUnknownDegree-2 branch 3 times, most recently from e63f4a8 to 956884d Compare March 29, 2022 22:51

ssiccha force-pushed the frss/AnSnRecogUnknownDegree-2 branch 2 times, most recently from 3b12114 to daceec3 Compare March 29, 2022 23:52

FriedrichRober force-pushed the frss/AnSnRecogUnknownDegree-2 branch 2 times, most recently from d45adbb to 7ba5ec6 Compare June 1, 2022 13:32

FriedrichRober force-pushed the frss/AnSnRecogUnknownDegree-2 branch 4 times, most recently from 85ca56f to deb2974 Compare November 7, 2022 03:36

fingolfin added the recog days 2025 label Dec 8, 2025

ssiccha added 2 commits December 8, 2025 15:23

Add option infoLevel to RECOG.TestGroup

f381cc7

Fix for howtowritearecogmethod.autodoc

2aed139

TWiedemann reviewed Mar 24, 2026

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TWiedemann linked an issue Mar 24, 2026 that may be closed by this pull request

SnAn naming algorithm #348

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SoongNoonien mentioned this pull request Apr 21, 2026

gap/SnAnBB.gi is unused, what to do with it? #17

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fingolfin reviewed May 12, 2026

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fingolfin and others added 4 commits May 12, 2026 11:17

Apply suggestions from code review

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Co-authored-by: Torben Wiedemann <7226617+TWiedemann@users.noreply.github.com> Co-authored-by: Max Horn <max@quendi.de>

remove some stuff

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Some renaming

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add a comment

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fingolfin added 3 commits May 12, 2026 17:23

missing word

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Merge branch 'master' into frss/AnSnRecogUnknownDegree-2

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fix test

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fingolfin reviewed May 12, 2026

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SoongNoonien and others added 4 commits May 19, 2026 10:32

Revise a comment about the meaning of some constants

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Co-authored-by: Torben Wiedemann <7226617+TWiedemann@users.noreply.github.com>

Apply suggestions from code review

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Co-authored-by: Torben Wiedemann <7226617+TWiedemann@users.noreply.github.com> Co-authored-by: Martin Wagner <martin.wagner.dev@gmail.com>

Merge branch 'master' into frss/AnSnRecogUnknownDegree-2

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Update gap/generic/SnAnUnknownDegree.gi

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		# Construct filter. In <Cite Key="C12"/> filter is called E.
		# In <Cite Key="JLNP13"/> filter is called `xi`.

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