Quellcode-Bibliothek simplerew.grp

#############################################################################
##
##  This file is part of GAP, a system for computational discrete algebra.
##  This file's author is Alexander Hulpke
##
##  Copyright of GAP belongs to its developers, whose names are too numerous
##  to list here. Please refer to the COPYRIGHT file for details.
##
##  SPDX-License-Identifier: GPL-2.0-or-later
##
##  Pre-computed confluent rewriting systems for certain simple groups,
##  that are not too large, but for which the calculation is slow.

##  They have been created by the function `SplitBNRewritingPresentation`,
##  typically with `weyl` and `borel` hand-selected and not computed by the
##  generic routine. This data could be verified by calling
##  `IsomorphismFpGroupForRewriting` on the respective simple group (which
##  will fetch the data from this file) and verifying that the associated
##  monoid presentation matches the generators, and is confluent.

##  They will be interpreted by the function `BuildRewritingFromData`.
##  The creator function `ConfluentRewritingData` is in a comment
##  in `lib.grpfpiso.gi`.

return
[
[[25308,"L",[2,37],"L2(37)"],
[(3,21)(4,22)(5,23)(6,24)(7,25)(8,26)(9,27)(10,28)(11,29)(12,30)
(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38),
(3,35,31,27,23,19,15,11,7)(4,36,32,28,24,20,16,12,8)(5,37,33,29,25,
21,17,13,9)(6,38,34,30,26,22,18,14,10),
(3,27,15)(4,28,16)(5,29,17)(6,30,18)(7,31,19)(8,32,20)(9,33,21)
(10,34,22)(11,35,23)(12,36,24)(13,37,25)(14,38,26),
(2,37,38,27,3,24,28,33,4,17,25,31,29,12,34,14,5,8,18,36,26,23,32,16,
30,11,13,7,35,22,15,10,6,21,9,20,19),
(1,2)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)
(22,38)(23,37)(24,36)(25,35)(26,34)(27,33)(28,32)(29,31)],10,
["b1","B1","b2","B2","b3","B3","b4","B4","w1","W1"],
[1,-1,2,-2,3,-3,4,-4,5,-5],[4,4,3,3,2,2,1,1,5,5],
[[2,1],[10,9],[12,0],[100,20],[14,34],[36,59],
[47,0],[102,53],[15,45],[37,0],[48,69],[103,42],
[16,56],[38,58],[49,59],[60,6],[71,0],[104,75],
[17,67],[39,69],[50,70],[61,0],[72,5],[105,64],
[18,89],[40,150051212],[51,353812919949505636],
[62,199718169425],[73,2510742701374],[95,0],[19,78],
[41,171487099],[52,404357622799435012],[63,228249336485],
[74,2196899863703],[85,0],[108,0],[1167,228],
[1178,227],[1169,2467500493673825045],
[1180,2472095466660182261],[1170,832102201],[1181,834050918],
[1171,21626624632313],[1182,21598093465252],
[1172,1678151371684],[1183,1680745114144],
[1175,204381358895012709664977172473917429],
[1186,178833689033136121261271986260843317],[12904,2516],
[13036,2504],[12906,8664543],[13038,8648438],
[12907,16215317894004390],[13039,16253292877362714],
[12908,316217686424764780],[13040,316635411241706345],
[12909,32752967446754236360],[13041,32702422743904306983],
[12912,538199994944134597566],[13044,470924995764699998430],
[142011,27684],[143474,27551],[142013,15321236711810],
[143476,15349767878871],[142014,1966648438160888490],
[143477,1962053465174531274],[142015,1108323],[143478,1109787],
[142016,1262768680],[143479,1260819963],
[142019,32164810514757092],[143482,36759783267268256],
[1562188,304532],[1578292,303068],[1562190,1395433443533],
[1578294,1392839701073],[1562191,100920161174],
[1578295,100684366405],[1562192,1477127561],
[1578296,1475178844],[1562193,86115],[1578297,86248],
[1562196,1886372793],[1578300,1650592665],[17184135,3349860],
[17361290,3333755],[17184137,95132825],[17361292,95309981],
[17184138,5178],[17361293,5166],
[17184139,421441732362711146259],[17361294,420885740631361923111],
[17184140,2233619475712335],[17361295,2237071746926728],
[17184143,32915822231400692220696932501507230727834],
[17361298,28801344452475605693628278228301977472458],
[189025552,36848468],[190974268,36671312],
[189025554,224735951514562023],[190974270,224318226697620458],
[189025555,6876877],[190974271,6892982],
[189025556,16226967291],[190974272,16248403179],
[189025557,24607789216194016],[190974273,24569814232835692],
[189025560,18580123535910244173542439364282744],
[190974276,16257608093921463915016269116933414],
[2079281139,405333156],[2100717026,403384439],[2079281141,590],
[2100717028,591],[2079281142,134010891685986],
[2100717029,134324734523658],[2079281143,100889],
[2100717030,100756],[2079281144,948736],[2100717031,947272],
[2079281147,150039237],[2100717034,171459153],
[22872092596,4458664724],[23107887364,4437228836],
[22872092598,27142505430412075502],
[23107887366,27193050133262004879],
[22872092599,237964461017467507386],
[23107887367,237408469286118284238],[22872092600,28785037385609667]
,[23107887368,28747062402251343],[22872092601,114619996],
[23107887369,114797152],[22872092604,171097242],
[23107887372,149838498],[251593018623,49045311972],
[254186761082,48809517203],[251593018625,787685],
[254186761084,786221],[251593018626,12211339502150],
[254186761085,12182808335089],[251593018627,237579028117779],
[254186761086,237892870955451],[251593018628,2972947522173118816],
[254186761087,2977542495159476032],
[251593018631,716344194596512420115328],
[254186761090,626801170274438360362608],
[2767523204920,539498431700],[2796054371980,536904689240],
[2767523204922,168533603829917],[2796054371982,168847446667589],
[2767523204923,626634],[2796054371983,625170],
[2767523204924,832],[2796054371984,833],
[2767523204925,18488196255592],[2796054371985,18459665088531],
[2767523204928,5920199954449201318422],
[2796054371988,5180174960336992351204],
[30442755254187,5934482748708],[30756598091858,5905951581647],
[30442755254189,126857585775],[30756598091860,126621791006],
[30442755254190,56833],[30756598091861,56966],
[30442755254191,1966056784755],[30756598091862,1963463042295],
[30442755254192,712],[30756598091863,711],
[30442755254195,9176995934049474215829760667],
[30756598091866,10487995353199049841561802811],
[334870307796124,65279310235796],[338322579010516,64965467398124],
[334870307796126,1046461082],[338322579010518,1048409799],
[334870307796127,1107528030462],[338322579010519,1110121772922],
[334870307796128,3478394550672412587],
[338322579010520,3482989523658769803],
[334870307796129,152559215607],[338322579010521,152795010376],
[334870307796132,75842941603637576914827651],
[338322579010524,86677647546988002666819413],
[3683573385757431,718072412593764],
[3721548369115754,714620141379371],
[3683573385757433,20430541046778365],
[3721548369115756,20392566063420041],
[3683573385757434,21582588116919844021],
[3721548369115757,21633132819769773398],
[3683573385757435,12191560],[3721548369115758,12207665],
[3683573385757436,360282641914296599968],
[3721548369115759,359726650182947376820],
[3683573385757439,100946955274547254372796033272],
[3721548369115762,115367948885196763504017912508],
[40519307243331808,7898796538531412],
[40937032060273372,7860821555173088],[40519307243331810,6497],
[40937032060273374,6509],[40519307243331811,1477572079760246],
[40937032060273375,1474119808545853],[40519307243331812,134284323],
[40937032060273376,134107167],[40519307243331813,13890455488],
[40937032060273377,13869019600],
[40519307243331816,2992347475581881108831880243533420945981],
[40937032060273380,2618304041134145970680207122720048841057],
[445712379676649955,86886761923845540],
[450307352663007170,86469037106903975],
[445712379676649957,298567559734532830529],
[450307352663007172,299123551465882053677],
[445712379676649958,75822810],[450307352663007173,75645654],
[445712379676649959,38312884760246467841],
[450307352663007174,38262340057396538464],
[445712379676649960,7828],[450307352663007175,7840],
[445712379676649963,3341797329099479],
[450307352663007178,2924072747775527],
[4902836176443149572,955754381162300948],
[4953380879293078948,951159408175943732],
[4902836176443149574,71607],[4953380879293078950,71474],
[4902836176443149575,469],[4953380879293078951,470],
[4902836176443149576,178496640208],
[4953380879293078952,178732434977],
[4902836176443149577,203056315973848],
[4953380879293078953,203370158811520],[4902836176443149580,11118],
[4953380879293078956,9786],
[53931197940874645359,10513298192785310436],
[54487189672223868506,10462753489935381059],
[53931197940874645361,1853869642129094],
[54487189672223868508,1857321913343487],
[53931197940874645362,9153124218],[54487189672223868509,9174560106]
,[53931197940874645363,9171],[54487189672223868510,9159],
[53931197940874645364,270685681378134184],
[54487189672223868511,270267956561192619],
[42811363313890182403,4447933850793785184],
[48927272358731637032,3891942119444562036],
[53931197940874645367,1689102139628202958932798534593273],
[54487189672223868514,1477964372174677986331993375037105],
[593243177349621099016,115646280120638414804],
[599359086394462553644,115090288389289191656],
[593243177349621099018,11532507797],
[599359086394462553646,11511071909],
[593243177349621099019,178368496834048297],
[599359086394462553647,178786221650989862],
[593243177349621099020,2616821580509969],
[599359086394462553648,2613369309295576],
[593243177349621099021,10436104],[599359086394462553649,10419999],
[593243177349621099024,27618099013755],
[599359086394462553652,24165849219145]]],
[[25920,"C",[2,3],"S4(3)"],
[(3,5)(6,9)(10,12)(11,16)(15,24)(17,19)(18,21)(20,39)(23,33)(25,34)
(26,38)(27,31)(28,30)(29,35)(32,40)(36,37),
(2,3,5)(7,12,10)(8,15,24)(11,20,31)(13,17,19)(14,23,33)(16,27,39)
(18,29,34)(21,25,35)(22,32,40)(26,37,30)(28,36,38),
(4,7,13)(6,10,17)(9,12,19)(15,25,36)(20,23,26)(24,34,37)(27,29,32)
(31,35,40)(33,38,39),(4,6,9)(7,10,12)(8,16,11)(13,17,19)
(14,21,18)(15,26,29)(20,32,25)(22,30,28)(23,27,36)(24,35,38)
(31,33,37)(34,40,39),(8,14,22)(11,18,28)(15,23,32)(16,21,30)
(20,29,36)(24,33,40)(25,26,27)(31,34,38)(35,37,39),
(2,4)(3,6,5,9)(7,13)(10,19,12,17)(11,15,16,24)(18,23,21,33)
(20,26,39,38)(25,37,34,36)(27,35,31,29)(28,32,30,40),
(1,2)(3,5)(4,8)(6,11)(7,14)(9,16)(10,18)(12,21)(13,22)(15,24)
(17,28)(19,30)(20,31)(23,34)(25,33)(26,38)(27,39)(29,35)(32,37)
(36,40),(3,5)(6,9)(10,12)(11,16)(15,24)(17,19)(18,21)(20,39)
(23,33)(25,34)(26,38)(27,31)(28,30)(29,35)(32,40)(36,37)],16,
["b1","B1","b2","B2","b3","B3","b4","B4","b5","B5","w1","W1",
"w2","W2","w3","W3"],
[1,-1,2,-2,3,-3,4,-4,5,-5,6,-6,7,-7,8,-8],
[5,5,4,4,3,3,2,2,1,1,6,6,6,6,6,6],
[[2,1],[12,28],[14,13],[15,1],[16,1],[18,0],
[188,28],[222,30],[20,69],[54,4],[71,0],
[190,130],[21,52],[55,0],[72,3],[22,86],
[56,46617],[73,46329],[90,6],[107,0],[226,166],
[23,103],[57,51258],[74,51548],[91,0],[108,5],
[24,137],[58,2723],[75,3013],[92,124],[109,125],
[126,8],[143,0],[194,79],[228,149],[25,120],
[59,3029],[76,2741],[93,141],[110,142],[127,0],
[144,7],[195,62],[26,154],[60,156],[77,157],
[94,158],[111,159],[128,160],[145,161],[162,10],
[179,0],[196,164],[230,98],[27,171],[61,173],
[78,174],[95,175],[112,176],[129,177],[146,178],
[163,0],[180,9],[231,115],[198,1],[234,0],
[3809,514],[3826,513],[3265,481],[3282,482],
[3267,787428],[3284,870661],[3275,29960],[3292,1637],
[3821,1381],[3838,1091],[58000,67280],[191,147],
[227,183],[229,132],[197,181],[3268,792052],
[3285,875863],[947253,1143765],[983667,1143652],
[985877,1141493],[985894,1141782],[952166,1143766],
[983956,1143635],[16100968,19442089],[16103178,19405386],
[16103195,19410299],[16101257,19441800],[16722216,19405273],
[16722233,19410186],[16184489,19442090],[16186699,19405387],
[16727129,19405256],[16186716,19410300],[16727146,19410169],
[16184778,19441801],[273716333,329889646],
[273716350,329973167],[273721246,329889357],
[273721263,329972878],[275136190,329889647],
[275136207,329973168],[275141103,329889358],
[275141120,329972879]]],
[[29120,"2B",8,"Sz(8)"],
[(3,4,5,6,7,8,9)(10,34,58,26,50,18,42)(11,36,61,30,55,24,49)
(12,37,62,31,56,25,43)(13,38,63,32,57,19,44)(14,39,64,33,51,20,45)
(15,40,65,27,52,21,46)(16,41,59,28,53,22,47)(17,35,60,29,54,23,48),
(2,29,6,32)(3,33,4,31)(5,26,8,30)(7,28,9,27)(10,63,14,65)
(11,64,12,61)(13,60,16,59)(15,58,17,62)(18,42,22,46)(19,43,20,44)
(21,45,24,48)(23,47,25,49)(34,52,38,51)(35,54,36,50)(37,55,40,57)
(39,53,41,56),(2,61,5,58)(3,65,9,59)(4,63,7,60)(6,64,8,62)
(10,32,13,30)(11,31,17,28)(12,33,15,27)(14,29,16,26)(18,52,21,55)
(19,54,25,56)(20,50,23,53)(22,51,24,57)(34,43,37,49)(35,42,41,45)
(36,46,39,48)(38,44,40,47),(2,41,4,40)(3,37,6,39)(5,35,7,38)
(8,36,9,34)(10,20,12,18)(11,22,14,19)(13,23,15,21)(16,25,17,24)
(26,53,28,55)(27,57,30,56)(29,50,31,52)(32,54,33,51)(42,59,44,62)
(43,58,46,60)(45,65,47,64)(48,63,49,61),
(2,6)(3,4)(5,8)(7,9)(10,14)(11,12)(13,16)(15,17)(18,22)(19,20)
(21,24)(23,25)(26,30)(27,28)(29,32)(31,33)(34,38)(35,36)(37,40)(39,41)
(42,46)(43,44)(45,48)(47,49)(50,54)(51,52)(53,56)(55,57)(58,62)(59,60)
(61,64)(63,65),(2,5)(3,9)(4,7)(6,8)(10,13)(11,17)(12,15)(14,16)
(18,21)(19,25)(20,23)(22,24)(26,29)(27,33)(28,31)(30,32)(34,37)(35,41)
(36,39)(38,40)(42,45)(43,49)(44,47)(46,48)(50,53)(51,57)(52,55)(54,56)
(58,61)(59,65)(60,63)(62,64),(2,4)(3,6)(5,7)(8,9)(10,12)(11,14)
(13,15)(16,17)(18,20)(19,22)(21,23)(24,25)(26,28)(27,30)(29,31)(32,33)
(34,36)(35,38)(37,39)(40,41)(42,44)(43,46)(45,47)(48,49)(50,52)(51,54)
(53,55)(56,57)(58,60)(59,62)(61,63)(64,65),
(1,24)(2,25)(3,36)(4,41)(5,28)(6,61)(7,31)(8,13)(9,64)(10,63)
(11,47)(12,14)(15,18)(16,46)(17,60)(19,53)(20,35)(21,44)(22,62)(23,33)
(26,34)(27,32)(29,42)(30,45)(37,59)(38,57)(39,56)(40,58)(48,52)(49,54)
(50,65)(51,55)],16,
["b1","B1","b2","B2","b3","B3","b4","B4","b5","B5","b6","B6",
"b7","B7","w1","W1"],
[1,-1,2,-2,3,-3,4,-4,5,-5,6,-6,7,-7,8,-8],
[3,3,2,2,2,2,2,2,1,1,1,1,1,1,4,4],
[[4,156],[6,192],[8,228],[10,9],[12,11],[14,13],
[16,15],[35,0],[256,4738306883],[19,0],
[257,5556061570],[20,46292],[37,67135],[54,9],
[22,56696],[39,56765],[56,67136],[90,11],[24,1142503],
[41,1498],[58,56766],[92,2725],[126,13],[26,3945],
[43,189],[60,156],[94,158],[128,160],[162,0],
[28,154],[45,223],[62,190],[96,192],[130,194],
[164,196],[198,0],[30,188],[47,3912],[64,224],
[98,226],[132,228],[166,230],[200,232],[234,0],
[270,0],[4387,4738307499],[4421,4738306271],
[4455,278723894],[4489,278723896],[4523,80551227488],
[4557,4738307495],[4388,5556061608],[4422,5556061610],
[4456,5556061502],[4490,5556060992],[4524,326827145],
[4558,94453047373],[4401,250353850192929],[4435,1592575748839],
[4469,50957492489],[4503,5613022926],[4537,4587717906],
[4571,1340218539665],[5220,614],[75192,4738307463],
[75770,4738306235],[76348,278723968],[76926,278723934],
[77504,16395525],[75804,4738306269],[76382,80551217050],
[76960,80551226876],[77538,4738307427],[76416,4738306881],
[76994,4738307459],[77572,278723962],[77028,4738307461],
[77606,278723964],[77640,278723930],[10440,307],
[75193,94453047339],[75771,94453047341],[76349,19225120],
[76927,94453047377],[77505,326827149],[75805,5556061606],
[76383,19225122],[76961,326827153],[77539,326827151],
[76417,5556060924],[76995,94453046727],[77573,94453047305],
[77029,326827111],[77607,326827077],[77641,5556061604],
[75206,4684201204],[75784,176306272],[76362,27577296291420],
[76940,5601496962],[77518,4738322814],[75818,23278539785685],
[76396,94451820279],[76974,1355424070631],[77552,5556145091],
[76430,3816757015],[77008,324159386],[77586,92812036591],
[77042,50955920945],[77620,95425992718],[77654,65706622553],
[1288703,80551206610],[1298529,80551227490],
[1308355,278723898],[1318181,16395521],[1299107,80551217014],
[1308933,80551226840],[1318759,4738307391],[1309511,16395523],
[1319337,964442],[1319915,278723970],[1299141,80551217048],
[1308967,80551226874],[1318793,4738307425],
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