add and integrate a SL2 in natural rep. recognition algorithm by Frank Lübeck #389
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## Include_ConstructiveRecognition_SL #389 +/- ##
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fingolfin
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| ## RECOG.RecogniseSL2NaturalOddCharUsingBSGS. | ||
| ## G must be SL(2,q) generated by 2x2 matrices over GF(q). | ||
| ## Note: does not work for q = 2, 3, 5. | ||
| ConRecogNaturalSL2 := function(G, f) |
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| ConRecogNaturalSL2 := function(G, f) | |
| RECOG.ConRecogNaturalSL2 := function(G, f) |
| for i in [1..Length(res.all)] do | ||
| if res.all[i]^res.basi <> res_old.all[i]^res_old.basi then | ||
| Print("Test failed for q = ", q, ", index i = ", i, " in the list \"all\" failed\n"); | ||
| valid := false; |
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| valid := false; | |
| valid := false; |
I think the indentation is still wrong here.
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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.