add and integrate a SL2 in natural rep. recognition algorithm by Frank Lübeck by Till-Eisen · Pull Request #389 · gap-packages/recog

Till-Eisen · 2026-02-17T09:17:16Z

Added Frank Lübeck's RecogNaturalSL2 algorithm as well as ConRecogNaturalSL2, which calls it and converts the output to the same format as RECOG.RecogniseSL2NaturalEvenChar / RECOG.RecogniseSL2NaturalOddCharUsingBSGS. ConRecogNaturalSL2 retries up to 100 times until the correct generators are found (usually takes very few attempts, i.e. 100 is a very high bound).
Also added test_ConRecogNaturalSL2 for testing: it accepts either a list of prime powers or an empty list — in the latter case a preset list of prime powers is tested automatically.

Note RecogNaturalSL2 does not work for q=2,3,5. In this case the old functions are called.

codecov · 2026-02-17T09:43:00Z

Codecov Report

❌ Patch coverage is 87.50000% with 28 lines in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (Include_ConstructiveRecognition_SL@5120658). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
...projective/constructive_recognition/SL/BaseCase.gi	88.18%	26 Missing ⚠️
gap/projective/constructive_recognition/SL/main.gi	0.00%	2 Missing ⚠️

Additional details and impacted files

@@                          Coverage Diff                          @@
##             Include_ConstructiveRecognition_SL     #389   +/-   ##
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  Coverage                                      ?   65.52%           
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  Files                                         ?       49           
  Lines                                         ?    20671           
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Files with missing lines	Coverage Δ
...ojective/constructive_recognition/utils/achieve.gi	`85.08% <100.00%> (ø)`
gap/projective/constructive_recognition/SL/main.gi	`41.91% <0.00%> (ø)`
...projective/constructive_recognition/SL/BaseCase.gi	`47.76% <88.18%> (ø)`

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SoongNoonien · 2026-03-03T09:24:42Z

I think we should just raise the minimum GAP version to 4.13. The problem with the 4.12 test failure is that the function DLog is apparently not available.

fingolfin · 2026-03-03T09:26:02Z

+## test function: compares ConRecogNaturalSL2 against the built-in recognition
+## note: does not work for q = 2, 3, 5
+## Input: either a list of prime powers or the empty list 
+## (then a preset list of prime powers is tested).
+test_ConRecogNaturalSL2 := function(input)


This needs to be turned into "proper" tests.

For example it could be moved into tst/utils.g or some other tst/BLAH.g file (could even be a new one); and a .tst file (either an existing one or a new one) should invoke this helper in a suitable way to ensure some of these tests are run as part of our CI.

Feel free to ask about details.

fingolfin · 2026-03-03T09:30:23Z

+      res_old := RECOG.RecogniseSL2NaturalOddCharUsingBSGS(G,f);
+    fi;
+    res := RECOG.ConRecogNaturalSL2(G,f);
+    ## compare all generators after change of basis


Ah so this test "only" checks that the old and new method get to the same result.

That maybe changes whether we should add these tests to the permanent tests, as the plan would be to delete RECOG.RecogniseSL2NaturalEvenChar and RECOG.RecogniseSL2NaturalOddCharUsingBSGS at some point.

Also, in the end, the "comparison" matrices can be reproduce much cheaper via

std := RECOG.MakeSL_StdGens(Characteristic(f),DegreeOverPrimeField(f),2,2);

So you could then compare res.all[i]^res.basi to those and not care about res_old at all.

fingolfin · 2026-03-03T10:53:33Z

      if IsEvenInt(q) then
-          std := RECOG.RecogniseSL2NaturalEvenChar(gm,f,false);
+          std := RECOG.ConRecogNaturalSL2(gm,f);
          ri!.comment := "PSL2Even";
      else
-          std := RECOG.RecogniseSL2NaturalOddCharUsingBSGS(gm,f);
+          std := RECOG.ConRecogNaturalSL2(gm,f);
          ri!.comment := "PSL2Odd";
      fi;


This could be merged together now, with ri!.comment := "PSL2";

fingolfin · 2026-03-03T10:55:22Z

-        else
-            resl2 := RECOG.RecogniseSL2NaturalOddCharUsingBSGS(Group(sl2genss),f);
-        fi;
+        resl2 := RECOG.ConRecogNaturalSL2(Group(sl2genss),f);


For fun I did a local benchmark:

gap> q:=2;; for i in [1..1000] do RECOG.RecogniseSL2NaturalOddCharUsingBSGS(SL(2,q),GF(q)); od; time; 608 gap> q:=2;; for i in [1..1000] do RECOG.RecogniseSL2NaturalEvenChar(SL(2,q),GF(q),false); od; time; 302

Note that I run the test a 1000 times in a loop to get better "accuracy. So 302 milliseconds for 1000 runs means 0.3 milliseconds per run. Not bad. And the specialized method indeed was faster.

Now you could try to compare this to your new code.

fingolfin · 2026-03-03T12:25:28Z

+## as RECOG.RecogniseSL2NaturalEvenChar and
+## RECOG.RecogniseSL2NaturalOddCharUsingBSGS.
+## G must be SL(2,q) generated by 2x2 matrices over GF(q).
+RECOG.ConRecogNaturalSL2 := function(G, f)


I've not yet looked at the content of this function, but I did run some benchmarks and they show that this function adds quite some overhead over Frank's code:

gap> q:=13^2;; for i in [1..1000] do RECOG.RecogniseSL2NaturalOddCharUsingBSGS(SL(2,q),GF(q)); od; time; 2432 gap> q:=13^2;; for i in [1..1000] do RECOG.ConRecogNaturalSL2(SL(2,q),GF(q)); od; time; 1202 gap> q:=13^2;; for i in [1..1000] do RECOG.RecogNaturalSL2(SL(2,q),q); od; time; 814

So it's still twice faster than the old code, but 50% slower than Frank's code.

In even char however it is almost three times slower than the old code, yet Frank's code is three times faster than the old code.

gap> q:=8;; for i in [1..1000] do RECOG.RecogniseSL2NaturalEvenChar(SL(2,q),GF(q),false); od; time; 1404 gap> q:=8;; for i in [1..1000] do RECOG.ConRecogNaturalSL2(SL(2,q),GF(q)); od; time; 4116 gap> q:=8;; for i in [1..1000] do RECOG.RecogNaturalSL2(SL(2,q),q); od; time; 513

... and add some comments (pointing out this needs documentation, and also an obvious bug in the code that would lead to an unexpected error if the code it is in was ever run)

... which made it depend on the characteristic. This corresponds to a change in our manuscript where it turned out we don't need this, and experiments validate this.

The GAP kernel already does that and this is way faster.

It is from Alnuth, and trivial to reimplement

Co-authored-by: Martin Wagner <martin.wagner.dev@gmail.com>

Co-authored-by: Max Horn <max@quendi.de>

…g old function

…ogNaturalSL2

TWiedemann · 2026-03-19T19:39:30Z

Closing this PR because it is replaced by #398.

Till-Eisen force-pushed the Include_ConstructiveRecognition_SL branch 2 times, most recently from 7abb134 to 84ff4f1 Compare February 17, 2026 10:29

fingolfin reviewed Feb 17, 2026

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Till-Eisen changed the title ~~add and integrate Frank Lübeck SL2 recognition algorithm~~ add and integrate Frank Lübeck SL2 in natural rep. recognition algorithm Feb 17, 2026

Till-Eisen changed the title ~~add and integrate Frank Lübeck SL2 in natural rep. recognition algorithm~~ add and integrate a SL2 in natural rep. recognition algorithm by Frank Lübeck Feb 17, 2026

Till-Eisen force-pushed the Include_ConstructiveRecognition_SL branch 2 times, most recently from 15c6c86 to 894600f Compare February 17, 2026 12:48

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Till-Eisen force-pushed the Include_ConstructiveRecognition_SL branch from eaf9760 to 3407986 Compare March 3, 2026 09:45

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Till-Eisen force-pushed the Include_ConstructiveRecognition_SL branch from 74e54f9 to 10a6ec2 Compare March 5, 2026 15:06

Till-Eisen force-pushed the Include_ConstructiveRecognition_SL branch from bd7e983 to 10a6ec2 Compare March 17, 2026 10:37

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fingolfin and others added 23 commits March 18, 2026 11:24

Factor out some duplicate code

1255ae7

Fix error in Computesl2Subspace

50d6e57

... and add some comments (pointing out this needs documentation, and also an obvious bug in the code that would lead to an unexpected error if the code it is in was ever run)

Get rid of GoalDim

7f02844

GoingUp: remove special case for initial stingray

7355a96

... which made it depend on the characteristic. This corresponds to a change in our manuscript where it turned out we don't need this, and experiments validate this.

Pass field not field size to ConvertToMatrixRep

3090b57

When compute a^b don't handle b=1 specially

90c6915

The GAP kernel already does that and this is way faster.

Some notes from debugging last year

9f3927f

Mark unused code

7ab16e1

Update PackageInfo.g

29c40db

Replace FieldOfPolynomial

218fb07

It is from Alnuth, and trivial to reimplement

Tweak RECOG.CheckPolynomialForSelfConjugate

77975de

Clarify info message

7ee7e3c

Add Frank Lübeck SL2 recognition algorithm

644d085

Update BaseCase with latest changes

d36b144

Improve readability and fix minor output bug

f29135a

Fall back to old algorithm for q=2,3,5

3077524

Add TODOs and minor cleanup

b47266c

main.gi: Use ConRecogNaturalSL2 instead of RecogniseSL2NaturalEvenChar

24a4a6f

Apply suggestion from @SoongNoonien

9c39296

Co-authored-by: Martin Wagner <martin.wagner.dev@gmail.com>

achieve.gi: Replace RecogniseSL2NaturalEvenChar with ConRecogNaturalSL2

2c1cdee

Apply suggestion from @fingolfin

14bf897

Co-authored-by: Max Horn <max@quendi.de>

Improve test: generate comparison matrices directly instead of callin…

b547501

…g old function

Apply bugfix from PR gap-packages#394 and remove retry loop in ConRec…

7c938f4

…ogNaturalSL2

Till-Eisen force-pushed the Include_ConstructiveRecognition_SL branch from 704cc15 to 7c938f4 Compare March 18, 2026 10:25

SoongNoonien closed this Mar 18, 2026

SoongNoonien reopened this Mar 18, 2026

Till-Eisen mentioned this pull request Mar 19, 2026

Add constructive recognition of SL(2,q) in natural representation 2.0 #398

Merged

TWiedemann closed this Mar 19, 2026

Till-Eisen deleted the Include_ConstructiveRecognition_SL branch March 20, 2026 11:55

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