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{
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"# Subgroup Lattice"
]
},
{
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"source": [
"This is a draft version of the Subgroup Lattice module, inspired by the XGAP version, and implements few features. At the moment is possible to explore the lattice by right clicking a node and explore its properties, and by generating all subgroups lattice."
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"true"
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"source": [
"LoadPackage(\"subgrouplattice\");"
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"text/plain": [
"Sym( [ 1 .. 5 ] )"
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Length( cls ) ] do nodes[i] := [ ]; for j in [ 1 .. len[i] ] do if len[i] = 1 then nodes[i][j] := Shape( ShapeType.DIAMOND, String( i ) ); else nodes[i][j] := Shape( ShapeType.CIRCLE, String( i ) ); fi; SetLayer( nodes[i][j], - Size( Representative( cls[i] ) ) ); for m in poset!.latticeType.contextMenus do knownArgs := [ poset, Representative( cls[i] ) ]; if m.group = true then Add( knownArgs, G ); fi; cb := Callback( m.func, knownArgs ); Add( nodes[i][j], Menu( m.name, cb ) ); od; if i = Length( cls ) and j = len[i] then SetTitle( nodes[i][j], \\\"G\\\" ); fi; Add( graphHasse, nodes[i][j] ); od; od; last := rec( o := 0, n := 0 ); for i in [ 1 .. Length( cls ) ] do for j in [ 1 .. len[i] ] do if Layer( nodes[i][j] ) <> last.o then last.o := Layer( nodes[i][j] ); last.n := last.n - 2; fi; SetLayer( nodes[i][j], last.n ); od; od; max := MaximalSubgroupsLattice( L ); for i in [ 1 .. Length( cls ) ] do for j in max[i] do rep := ClassElementLattice( cls[i], 1 ); for k in [ 1 .. len[i] ] do if k = 1 then z := j[2]; else t := cls[i]!.normalizerTransversal[k]; z := ClassElementLattice( cls[j[1]], 1 ); z := cls[j[1]]!.normalizerTransversal[j[2]] * t; z := PositionCanonical( cls[j[1]]!.normalizerTransversal, z ); fi; Add( graphHasse, Link( nodes[j[1]][z], nodes[i][k] ) ); od; od; od; return Draw( poset ); end, group := true, multiple := false, name := \\\"All Subgroups\\\" )\"],\"trivial\" : true},\"menus\" : {\"FC6A9944CD86B443E7C342BF378CDD1C0\" : {\"callback\" : {},\"id\" : \"FC6A9944CD86B443E7C342BF378CDD1C0\",\"menus\" : {\"F04453510D96946ED4C05ABC611B6675E\" : {\"callback\" : {\"func\" : \"unknown\",\"id\" : \"FB3FEBDF7E7964C8624D124FF694D973A\",\"knownArgs\" : [\"<object>\",\"SymmetricGroup( [ 1 .. 5 ] )\"],\"requiredArgs\" : {},\"trigger\" : \"click\"},\"id\" : \"F04453510D96946ED4C05ABC611B6675E\",\"menus\" : {},\"title\" : \"All Subgroups\"}},\"title\" : \"Subgroup Lattice\"}},\"messages\" : {\"F8F419FE8CFAC4BB2E4B26A36CFD237A4\" : {\"callback\" : {\"func\" : \"Remove\",\"id\" : \"FB06212CEB92941256CD0C925F3CC61FD\",\"knownArgs\" : [\"<object>\",\"<object>\"],\"requiredArgs\" : {},\"trigger\" : \"click\"},\"id\" : \"F8F419FE8CFAC4BB2E4B26A36CFD237A4\",\"text\" : \"There are 16 levels in this Group.\",\"title\" : \"\",\"type\" : \"default\"}},\"texTypesetting\" : true,\"title\" : \"GraphicSubgroupLattice\",\"width\" : 800,\"zoomToFit\" : true},\"mime\" : \"application\\/vnd.francy+json\",\"version\" : \"1.2.4\"}"
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"source": [
"G := SymmetricGroup(5); #G := PSL(2, 7); #G := DihedralGroup(44);\n",
"GraphicSubgroupLattice(G);"
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[ Dauer der Verarbeitung: 0.38 Sekunden
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]
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