Quelle  threeelorders.gi   Sprache: unbekannt

# RECOG.grouplist is used by RECOG.findchar, which uses the three largest
# element orders to find the characteristic of its input lie type group.
# RECOG.grouplist contains entries of the form
#    [m1, m2, grp],
# where m1 and m2 are the largest element orders found by sampling
# a suitable number of random elements, and grp indicates a group as below.
#
# Note that RECOG.findchar first uses the three largest element orders to
# handle some (or even all?) cases which are not already uniquely determined by
# the largest two. Thus we only store the two largest element orders in
# RECOG.grouplist.
# grp is of the form:
#    ["l",n,q] <-> L_n(q)
#    ["G2",q]  <-> G_2(q)
#    ["2G2",q] <-> G_2(q)
#    ...
# The types used below are:
#  2B2, 2E6, 2F4, 2G2, 3D4, E6, E7, E8, F4, G2, l, o, o+, o-, s, u
#
# FIXME: where does this table come from? How was it generated?
# The mathematics underpinning this file seems to come from [KS09].
#
# Note: It contains many groups multiple times, e.g. it contains
# these two entries:
#   [751,376,["l",2,751]]
#   [376,375,["l",2,751]]
# In fact, some groups occur even more often. The record is set
# by ["s",14,3] and ["s",16,3], which each occur 19 times.
#
# So, what does that mean? Was the table maybe generated by "random
# sampling" of group elements itself?
#
# Note that misc/twoelorders.gi contains an older (?) version of this code.
RECOG.grouplist:=
[[3,2,["l",2,5]],[4,3,["l",2,7]],[5,3,["l",2,4]],
[5,3,["l",2,5]],[5,3,["s",4,2]],[5,4,["l",2,9]],
[5,4,["s",4,3]],[6,5,["l",2,11]],[6,5,["s",4,3]],
[7,2,["2G2",3]],[7,3,["2G2",3]],[7,3,["G2",2]],
[7,3,["l",3,2]],[7,4,["G2",2]],[7,4,["l",2,7]],
[7,4,["l",3,2]],[7,5,["l",3,4]],[7,6,["G2",2]],
[7,6,["l",2,13]],[8,7,["G2",2]],[8,7,["u",3,3]],
[8,7,["u",3,5]],[8,7,["u",4,3]],[9,5,["s",4,3]],
[9,5,["u",4,2]],[9,6,["s",4,3]],[9,6,["u",4,2]],
[9,7,["2G2",3]],[9,7,["l",2,8]],[9,8,["l",2,17]],
[9,8,["u",4,3]],[10,8,["u",3,5]],[10,9,["l",2,19]],
[11,6,["l",2,11]],[12,5,["s",4,3]],[12,6,["s",4,3]],
[12,7,["G2",2]],[12,8,["G2",2]],[12,8,["u",3,3]],
[12,8,["u",4,3]],[12,9,["s",4,3]],[12,9,["u",4,2]],
[12,9,["u",4,3]],[12,11,["l",2,23]],[13,5,["2F4",2]],
[13,6,["2F4",2]],[13,7,["2B2",8]],[13,7,["l",2,13]],
[13,8,["l",3,3]],[13,8,["G2",3]],[13,8,["2F4",2]],
[13,9,["G2",3]],[13,10,["2F4",2]],[13,12,["2F4",2]],
[13,12,["G2",3]],[13,12,["l",2,25]],[13,12,["s",4,5]],
[14,13,["l",2,27]],[15,7,["l",4,2]],[15,9,["o+",8,2]],
[15,9,["s",6,2]],[15,10,["o+",8,2]],[15,10,["s",6,2]],
[15,11,["u",5,2]],[15,11,["u",6,2]],[15,12,["o+",8,2]],
[15,12,["s",6,2]],[15,12,["u",5,2]],[15,12,["u",6,2]],
[15,13,["s",4,5]],[15,13,["u",3,4]],[15,14,["l",2,29]],
[16,13,["2F4",2]],[16,15,["l",2,31]],[17,9,["l",2,17]],
[17,15,["l",2,16]],[17,15,["s",4,4]],[18,15,["u",5,2]],
[18,15,["u",6,2]],[19,10,["l",2,19]],[19,16,["l",3,7]],
[19,18,["l",2,37]],[20,13,["l",4,3]],[20,13,["s",4,5]],
[20,14,["o",7,3]],[20,14,["o+",8,3]],[20,14,["s",6,3]],
[20,15,["o",7,3]],[20,15,["o+",8,3]],[20,15,["s",4,5]],
[20,15,["s",6,3]],[20,18,["o",7,3]],[20,18,["o+",8,3]],
[20,18,["s",6,3]],[21,13,["3D4",2]],[21,14,["3D4",2]],
[21,15,["G2",4]],[21,17,["F4",2]],[21,17,["o-",8,2]],
[21,17,["s",8,2]],[21,18,["3D4",2]],[21,18,["F4",2]],
[21,18,["s",8,2]],[21,19,["u",3,8]],[21,20,["F4",2]],
[21,20,["l",2,41]],[21,20,["s",8,2]],[22,21,["l",2,43]],
[23,12,["l",2,23]],[24,20,["s",6,3]],[24,21,["F4",2]],
[24,21,["s",8,2]],[24,23,["l",2,47]],[25,24,["l",2,49]],
[25,24,["s",4,7]],[27,26,["l",2,53]],[28,21,["3D4",2]],
[28,21,["F4",2]],[28,24,["F4",2]],[28,25,["s",4,7]],
[29,15,["l",2,29]],[30,13,["s",4,5]],[30,15,["s",4,5]],
[30,20,["s",4,5]],[30,20,["s",6,3]],[30,21,["F4",2]],
[30,21,["o-",8,2]],[30,21,["s",8,2]],[30,24,["F4",2]],
[30,24,["s",6,3]],[30,24,["s",8,2]],[30,28,["F4",2]],
[30,29,["l",2,59]],[31,16,["l",2,31]],[31,21,["l",5,2]],
[31,24,["l",3,5]],[31,24,["G2",5]],[31,25,["G2",5]],
[31,30,["G2",5]],[31,30,["l",2,61]],[33,31,["l",2,32]],
[34,33,["l",2,67]],[35,33,["2E6",2]],[35,33,["o-",10,2]],
[36,20,["s",6,3]],[36,24,["s",6,3]],[36,30,["s",6,3]],
[36,35,["l",2,71]],[37,19,["l",2,37]],[37,26,["2G2",27]],
[37,36,["l",2,73]],[39,31,["l",4,5]],[40,37,["u",3,11]],
[40,39,["l",2,79]],[41,21,["l",2,41]],[41,31,["2B2",32]],
[41,40,["l",2,81]],[41,40,["s",4,9]],[42,25,["s",4,7]],
[42,28,["s",4,7]],[42,41,["l",2,83]],[43,22,["l",2,43]],
[44,40,["u",3,11]],[45,44,["l",2,89]],[47,24,["l",2,47]],
[48,43,["u",3,7]],[49,48,["l",2,97]],[51,45,["o+",10,2]],
[51,45,["s",10,2]],[51,50,["l",2,101]],[52,41,["o",9,3]],
[52,41,["o-",8,3]],[52,41,["s",8,3]],[52,42,["o",9,3]],
[52,42,["s",8,3]],[52,45,["o",9,3]],[52,45,["s",8,3]],
[52,51,["l",2,103]],[53,27,["l",2,53]],
[54,53,["l",2,107]],[55,54,["l",2,109]],
[56,25,["s",4,7]],[56,28,["s",4,7]],[56,42,["s",4,7]],
[56,48,["u",3,7]],[57,48,["G2",7]],[57,49,["G2",7]],
[57,56,["G2",7]],[57,56,["l",2,113]],[59,30,["l",2,59]],
[60,51,["o+",10,2]],[60,51,["s",10,2]],[60,52,["o",9,3]],
[60,52,["o-",8,3]],[60,52,["s",8,3]],[61,31,["l",2,61]],
[61,56,["l",3,13]],[61,60,["l",2,121]],
[61,60,["s",4,11]],[63,31,["l",6,2]],[63,45,["u",7,2]],
[63,52,["u",4,5]],[63,60,["u",4,5]],[63,60,["u",7,2]],
[63,62,["l",2,125]],[64,63,["l",2,127]],
[65,51,["u",4,4]],[65,51,["u",5,4]],[65,63,["l",2,64]],
[65,63,["s",4,8]],[66,61,["s",4,11]],[66,63,["u",7,2]],
[66,65,["l",2,131]],[67,34,["l",2,67]],
[69,68,["l",2,137]],[70,69,["l",2,139]],
[71,36,["l",2,71]],[72,52,["s",8,3]],[72,60,["s",8,3]],
[73,37,["l",2,73]],[73,63,["l",3,8]],[73,63,["G2",8]],
[75,74,["l",2,149]],[76,75,["l",2,151]],
[78,52,["s",8,3]],[78,60,["s",8,3]],[78,63,["o",7,5]],
[78,63,["s",6,5]],[78,65,["o",7,5]],[78,65,["s",6,5]],
[78,72,["s",8,3]],[79,40,["l",2,79]],[79,78,["l",2,157]],
[80,61,["u",5,3]],[80,65,["o-",10,3]],[80,73,["u",3,9]],
[82,81,["l",2,163]],[83,42,["l",2,83]],[84,52,["s",8,3]],
[84,60,["s",8,3]],[84,72,["s",8,3]],[84,78,["s",8,3]],
[84,80,["o-",10,3]],[84,80,["u",5,3]],
[84,83,["l",2,167]],[85,63,["l",4,4]],[85,65,["s",6,4]],
[85,84,["l",2,169]],[85,84,["s",4,13]],[86,75,["u",4,7]],
[86,84,["u",4,7]],[87,86,["l",2,173]],[89,45,["l",2,89]],
[90,52,["s",8,3]],[90,60,["s",8,3]],[90,72,["s",8,3]],
[90,78,["s",8,3]],[90,84,["s",8,3]],[90,89,["l",2,179]],
[91,80,["l",3,9]],[91,80,["G2",9]],[91,85,["l",3,16]],
[91,85,["s",4,13]],[91,90,["l",2,181]],
[93,65,["o-",12,2]],[93,84,["o-",12,2]],[93,91,["E6",2]],
[96,91,["u",3,17]],[96,95,["l",2,191]],
[97,49,["l",2,97]],[97,96,["l",2,193]],
[99,98,["l",2,197]],[100,99,["l",2,199]],
[101,51,["l",2,101]],[102,93,["o-",12,2]],
[102,96,["u",3,17]],[103,52,["l",2,103]],
[104,73,["3D4",3]],[104,78,["3D4",3]],[104,82,["F4",3]],
[104,84,["3D4",3]],[104,84,["F4",3]],[104,90,["F4",3]],
[105,85,["o+",12,2]],[105,93,["s",12,2]],
[105,102,["s",12,2]],[106,105,["l",2,211]],
[107,54,["l",2,107]],[109,55,["l",2,109]],
[109,91,["2F4",8]],[110,61,["s",4,11]],
[110,66,["s",4,11]],[112,111,["l",2,223]],
[113,57,["l",2,113]],[114,113,["l",2,227]],
[115,114,["l",2,229]],[117,116,["l",2,233]],
[120,78,["s",6,5]],[120,104,["F4",3]],
[120,105,["s",12,2]],[120,119,["l",2,239]],
[121,104,["l",5,3]],[121,120,["l",2,241]],
[122,91,["u",6,3]],[122,120,["u",6,3]],
[122,121,["l",2,243]],[126,93,["E6",2]],
[126,125,["l",2,251]],[127,64,["l",2,127]],
[127,105,["l",7,2]],[127,120,["l",3,19]],
[129,99,["u",8,2]],[129,99,["u",9,2]],
[129,126,["u",8,2]],[129,126,["u",9,2]],
[129,127,["l",2,128]],[129,128,["l",2,257]],
[130,78,["s",6,5]],[130,120,["s",6,5]],
[131,66,["l",2,131]],[132,61,["s",4,11]],
[132,66,["s",4,11]],[132,110,["s",4,11]],
[132,129,["u",8,2]],[132,129,["u",9,2]],
[132,131,["l",2,263]],[133,120,["l",3,11]],
[133,120,["G2",11]],[133,121,["G2",11]],
[133,132,["G2",11]],[135,134,["l",2,269]],
[136,135,["l",2,271]],[137,69,["l",2,137]],
[139,70,["l",2,139]],[139,138,["l",2,277]],
[141,140,["l",2,281]],[142,141,["l",2,283]],
[145,127,["2B2",128]],[145,144,["l",2,289]],
[145,144,["s",4,17]],[147,146,["l",2,293]],
[149,75,["l",2,149]],[151,76,["l",2,151]],
[153,145,["s",4,17]],[154,153,["l",2,307]],
[156,78,["o+",8,5]],[156,85,["s",4,13]],
[156,91,["s",4,13]],[156,155,["l",2,311]],
[157,79,["l",2,157]],[157,156,["l",2,313]],
[159,158,["l",2,317]],[163,82,["l",2,163]],
[164,140,["o+",10,3]],[164,140,["o",11,3]],
[164,140,["s",10,3]],[164,156,["o+",10,3]],
[164,156,["o",11,3]],[164,156,["s",10,3]],
[166,165,["l",2,331]],[167,84,["l",2,167]],
[168,157,["u",3,13]],[169,168,["l",2,337]],
[172,171,["l",2,343]],[173,87,["l",2,173]],
[174,173,["l",2,347]],[175,174,["l",2,349]],
[176,169,["u",3,23]],[177,176,["l",2,353]],
[179,90,["l",2,179]],[180,164,["o",11,3]],
[180,164,["s",10,3]],[180,179,["l",2,359]],
[181,91,["l",2,181]],[181,180,["l",2,361]],
[181,180,["s",4,19]],[182,85,["s",4,13]],
[182,91,["s",4,13]],[182,121,["l",6,3]],
[182,156,["s",4,13]],[182,168,["u",3,13]],
[183,168,["G2",13]],[183,169,["G2",13]],[183,182,["G2",13]],
[184,176,["u",3,23]],[184,183,["l",2,367]],
[187,186,["l",2,373]],[190,181,["s",4,19]],
[190,189,["l",2,379]],[191,96,["l",2,191]],
[192,191,["l",2,383]],[193,97,["l",2,193]],
[195,165,["o+",14,2]],[195,186,["o+",14,2]],
[195,194,["l",2,389]],[197,99,["l",2,197]],
[199,100,["l",2,199]],[199,198,["l",2,397]],
[200,171,["l",4,7]],[200,172,["o",7,7]],
[200,172,["s",6,7]],[200,175,["o",7,7]],
[200,175,["s",6,7]],[201,200,["l",2,401]],
[204,195,["o+",14,2]],[205,182,["l",4,9]],
[205,204,["l",2,409]],[210,209,["l",2,419]],
[211,106,["l",2,211]],[211,210,["l",2,421]],
[216,215,["l",2,431]],[217,208,["l",3,25]],
[217,216,["l",2,433]],[220,219,["l",2,439]],
[222,221,["l",2,443]],[223,112,["l",2,223]],
[225,224,["l",2,449]],[227,114,["l",2,227]],
[229,115,["l",2,229]],[229,228,["l",2,457]],
[231,230,["l",2,461]],[232,231,["l",2,463]],
[233,117,["l",2,233]],[234,164,["s",10,3]],
[234,180,["s",10,3]],[234,233,["l",2,467]],
[239,120,["l",2,239]],[240,164,["s",10,3]],
[240,180,["s",10,3]],[240,234,["s",10,3]],
[240,239,["l",2,479]],[241,121,["l",2,241]],
[244,243,["l",2,487]],[246,164,["s",10,3]],
[246,180,["s",10,3]],[246,234,["s",10,3]],
[246,240,["s",10,3]],[246,245,["l",2,491]],
[250,249,["l",2,499]],[251,126,["l",2,251]],
[252,164,["s",10,3]],[252,180,["s",10,3]],
[252,234,["s",10,3]],[252,240,["s",10,3]],
[252,246,["s",10,3]],[252,251,["l",2,503]],
[255,85,["o+",8,4]],[255,155,["o-",14,2]],
[255,195,["s",14,2]],[255,204,["s",14,2]],
[255,210,["o-",14,2]],[255,210,["s",14,2]],
[255,217,["E7",2]],[255,217,["l",8,2]],
[255,241,["u",3,16]],[255,252,["E7",2]],
[255,254,["l",2,509]],[257,129,["l",2,257]],
[257,255,["l",2,256]],[257,255,["s",4,16]],
[260,205,["o+",12,3]],[261,260,["l",2,521]],
[262,261,["l",2,523]],[263,132,["l",2,263]],
[265,264,["l",2,529]],[265,264,["s",4,23]],
[269,135,["l",2,269]],[271,136,["l",2,271]],
[271,242,["2G2",243]],[271,270,["l",2,541]],
[272,145,["s",4,17]],[272,153,["s",4,17]],
[273,255,["G2",16]],[274,273,["l",2,547]],
[276,265,["s",4,23]],[277,139,["l",2,277]],
[279,278,["l",2,557]],[280,271,["u",3,29]],
[281,141,["l",2,281]],[282,281,["l",2,563]],
[283,142,["l",2,283]],[285,284,["l",2,569]],
[286,285,["l",2,571]],[289,288,["l",2,577]],
[290,280,["u",3,29]],[293,147,["l",2,293]],
[294,293,["l",2,587]],[297,296,["l",2,593]],
[300,299,["l",2,599]],[301,300,["l",2,601]],
[304,303,["l",2,607]],[306,145,["s",4,17]],
[306,153,["s",4,17]],[306,272,["s",4,17]],
[307,154,["l",2,307]],[307,288,["l",3,17]],
[307,288,["G2",17]],[307,289,["G2",17]],
[307,306,["G2",17]],[307,306,["l",2,613]],
[309,308,["l",2,617]],[310,309,["l",2,619]],
[311,156,["l",2,311]],[313,157,["l",2,313]],
[313,312,["l",2,625]],[313,312,["s",4,25]],
[315,241,["3D4",4]],[315,257,["F4",4]],
[315,257,["o-",8,4]],[315,257,["s",8,4]],
[316,315,["l",2,631]],[317,159,["l",2,317]],
[321,320,["l",2,641]],[322,321,["l",2,643]],
[324,323,["l",2,647]],[327,326,["l",2,653]],
[330,329,["l",2,659]],[331,166,["l",2,331]],
[331,320,["l",3,31]],[331,330,["l",2,661]],
[333,305,["u",4,11]],[333,330,["u",4,11]],
[336,200,["s",6,7]],[337,169,["l",2,337]],
[337,336,["l",2,673]],[339,338,["l",2,677]],
[341,315,["l",5,4]],[341,331,["u",3,32]],
[342,181,["s",4,19]],[342,190,["s",4,19]],
[342,341,["l",2,683]],[346,345,["l",2,691]],
[347,174,["l",2,347]],[349,175,["l",2,349]],
[350,200,["s",6,7]],[350,336,["s",6,7]],
[351,350,["l",2,701]],[353,177,["l",2,353]],
[355,354,["l",2,709]],[359,180,["l",2,359]],
[360,343,["u",3,19]],[360,359,["l",2,719]],
[364,363,["l",2,727]],[365,328,["u",4,9]],
[365,364,["l",2,729]],[365,364,["s",4,27]],
[367,184,["l",2,367]],[367,366,["l",2,733]],
[370,369,["l",2,739]],[372,313,["o",9,5]],
[372,313,["o-",8,5]],[372,313,["s",8,5]],
[372,315,["o",9,5]],[372,315,["s",8,5]],
[372,371,["l",2,743]],[373,187,["l",2,373]],
[376,375,["l",2,751]],[379,190,["l",2,379]],
[379,378,["l",2,757]],[380,181,["s",4,19]],
[380,190,["s",4,19]],[380,342,["s",4,19]],
[380,360,["u",3,19]],[381,315,["o-",16,2]],
[381,360,["G2",19]],[381,361,["G2",19]],
[381,372,["o-",16,2]],[381,380,["G2",19]],
[381,380,["l",2,761]],[383,192,["l",2,383]],
[385,384,["l",2,769]],[387,386,["l",2,773]],
[389,195,["l",2,389]],[390,372,["o",9,5]],
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