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# This file was created automatically, do not edit!
#############################################################################
##
#W hamilcyc.tst GAP 4 package CTblLib Thomas Breuer
##
## This file contains the GAP code of examples in the package
## documentation files.
##
## In order to run the tests, one starts GAP from the 'tst' subdirectory
## of the 'pkg/ctbllib' directory, and calls 'Test( "hamilcyc.tst" );'.
##
gap> LoadPackage( "CTblLib", false );
true
gap> save:= SizeScreen();;
gap> SizeScreen( [ 72 ] );;
gap> START_TEST( "hamilcyc.tst" );
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> oldinterval:= data.replayInterval;
> data.replayInterval:= 1;
> fi;
## doc2/hamilcyc.xml (140-148)
gap> if not CompareVersionNumbers( GAPInfo.Version, "4.5" ) then
> Error( "need GAP in version at least 4.5" );
> fi;
gap> LoadPackage( "ctbllib", "1.2", false );
true
gap> LoadPackage( "tomlib", "1.1.1", false );
true
## doc2/hamilcyc.xml (586-598)
gap> IsGeneratorsOfTransPermGroup:= function( G, list )
> local S;
>
> if not IsTransitive( G ) then
> Error( "<G> must be transitive on its moved points" );
> fi;
> S:= SubgroupNC( G, list );
>
> return IsTransitive( S, MovedPoints( G ) )
> and Size( S ) = Size( G );
> end;;
## doc2/hamilcyc.xml (689-763)
gap> BindGlobal( "VertexDegreesGeneratingGraph",
> function( G, classes, normalsubgroups )
> local nccl, matrix, cents, powers, normalsubgroupspos, i, j, g_i,
> nsg, g_j, gen, pair, d, pow;
>
> if not IsTransitive( G ) then
> Error( "<G> must be transitive on its moved points" );
> fi;
>
> classes:= Filtered( classes,
> C -> Order( Representative( C ) ) <> 1 );
> nccl:= Length( classes );
> matrix:= [];
> cents:= [];
> powers:= [];
> normalsubgroupspos:= [];
> for i in [ 1 .. nccl ] do
> matrix[i]:= [];
> if IsBound( powers[i] ) then
> # The i-th row equals the earlier row 'powers[i]'.
> for j in [ 1 .. i ] do
> matrix[i][j]:= matrix[ powers[i] ][j];
> matrix[j][i]:= matrix[j][ powers[i] ];
> od;
> else
> # We have to compute the values.
> g_i:= Representative( classes[i] );
> nsg:= Filtered( [ 1 .. Length( normalsubgroups ) ],
> i -> g_i in normalsubgroups[i] );
> normalsubgroupspos[i]:= nsg;
> cents[i]:= Centralizer( G, g_i );
> for j in [ 1 .. i ] do
> g_j:= Representative( classes[j] );
> if IsBound( powers[j] ) then
> matrix[i][j]:= matrix[i][ powers[j] ];
> matrix[j][i]:= matrix[ powers[j] ][i];
> elif not IsEmpty( Intersection( nsg, normalsubgroupspos[j] ) )
> or ( Order( g_i ) = 2 and Order( g_j ) = 2
> and not IsDihedralGroup( G ) ) then
> matrix[i][j]:= 0;
> matrix[j][i]:= 0;
> else
> # Compute $d(g_i, g_j^G)$.
> gen:= 0;
> for pair in DoubleCosetRepsAndSizes( G, cents[j],
> cents[i] ) do
> if IsGeneratorsOfTransPermGroup( G,
> [ g_i, g_j^pair[1] ] ) then
> gen:= gen + pair[2];
> fi;
> od;
> matrix[i][j]:= gen / Size( cents[j] );
> if i <> j then
> matrix[j][i]:= gen / Size( cents[i] );
> fi;
> fi;
> od;
>
> # For later, provide information about algebraic conjugacy.
> for d in Difference( PrimeResidues( Order( g_i ) ), [ 1 ] ) do
> pow:= g_i^d;
> for j in [ i+1 .. nccl ] do
> if not IsBound( powers[j] ) and pow in classes[j] then
> powers[j]:= i;
> break;
> fi;
> od;
> od;
> fi;
> od;
>
> return matrix;
> end );
## doc2/hamilcyc.xml (843-883)
gap> DeclareAttribute( "PrimitivePermutationCharacters",
> IsCharacterTable );
gap> InstallOtherMethod( PrimitivePermutationCharacters,
> [ IsCharacterTable ],
> function( tbl )
> local maxes, i, fus, poss, tom, G;
>
> if HasMaxes( tbl ) then
> maxes:= List( Maxes( tbl ), CharacterTable );
> for i in [ 1 .. Length( maxes ) ] do
> fus:= GetFusionMap( maxes[i], tbl );
> if fus = fail then
> fus:= PossibleClassFusions( maxes[i], tbl );
> poss:= Set( fus,
> map -> InducedClassFunctionsByFusionMap(
> maxes[i], tbl,
> [ TrivialCharacter( maxes[i] ) ], map )[1] );
> if Length( poss ) = 1 then
> maxes[i]:= poss[1];
> else
> return fail;
> fi;
> else
> maxes[i]:= TrivialCharacter( maxes[i] )^tbl;
> fi;
> od;
> return maxes;
> elif HasFusionToTom( tbl ) then
> tom:= TableOfMarks( tbl );
> maxes:= MaximalSubgroupsTom( tom );
> return PermCharsTom( tbl, tom ){ maxes[1] };
> elif HasUnderlyingGroup( tbl ) then
> G:= UnderlyingGroup( tbl );
> return List( MaximalSubgroupClassReps( G ),
> M -> TrivialCharacter( M )^tbl );
> fi;
>
> return fail;
> end );
## doc2/hamilcyc.xml (915-926)
gap> LowerBoundsVertexDegrees:= function( classlengths, prim )
> local sizes, nccl;
>
> nccl:= Length( classlengths );
> return List( [ 2 .. nccl ],
> i -> List( [ 2 .. nccl ],
> j -> Maximum( 0, classlengths[j] - Sum( prim,
> pi -> classlengths[j] * pi[j] * pi[i]
> / pi[1] ) ) ) );
> end;;
## doc2/hamilcyc.xml (974-991)
gap> LowerBoundsVertexDegreesOfClosure:= function( classlengths, bounds )
> local delta, newbounds, size, i, j;
>
> delta:= List( bounds, Sum );
> newbounds:= List( bounds, ShallowCopy );
> size:= Sum( classlengths );
> for i in [ 1 .. Length( bounds ) ] do
> for j in [ 1 .. Length( bounds ) ] do
> if delta[i] + delta[j] >= size - 1 then
> newbounds[i][j]:= classlengths[ j+1 ];
> fi;
> od;
> od;
>
> return newbounds;
> end;;
## doc2/hamilcyc.xml (1066-1112)
gap> CheckCriteriaOfPosaAndChvatal:= function( classlengths, bounds )
> local size, degs, addinterval, badForPosa, badForChvatal1, pos,
> half, i, low1, upp2, upp1, low2, badForChvatal, interval1,
> interval2;
>
> size:= Sum( classlengths );
> degs:= List( [ 2 .. Length( classlengths ) ],
> i -> [ Sum( bounds[ i-1 ] ), classlengths[i], i ] );
> Sort( degs );
>
> addinterval:= function( intervals, low, upp )
> if low <= upp then
> Add( intervals, [ low, upp ] );
> fi;
> end;
>
> badForPosa:= [];
> badForChvatal1:= [];
> pos:= 1;
> half:= Int( size / 2 ) - 1;
> for i in [ 1 .. Length( degs ) ] do
> # We have pos = c_1 + c_2 + \cdots + c_{i-1} + 1
> low1:= Maximum( pos, degs[i][1] ); # L_i
> upp2:= Minimum( half, size-1-pos, size-1-degs[i][1] ); # U'_i
> pos:= pos + degs[i][2];
> upp1:= Minimum( half, pos-1 ); # U_i
> low2:= Maximum( 1, size-pos ); # L'_i
> addinterval( badForPosa, low1, upp1 );
> addinterval( badForChvatal1, low2, upp2 );
> od;
>
> # Intersect intervals.
> badForChvatal:= [];
> for interval1 in badForPosa do
> for interval2 in badForChvatal1 do
> addinterval( badForChvatal,
> Maximum( interval1[1], interval2[1] ),
> Minimum( interval1[2], interval2[2] ) );
> od;
> od;
>
> return rec( badForPosa:= badForPosa,
> badForChvatal:= Set( badForChvatal ),
> data:= degs );
> end;;
## doc2/hamilcyc.xml (1144-1180)
gap> HamiltonianCycleInfo:= function( classlengths, bounds )
> local i, result, res, oldbounds;
>
> i:= 0;
> result:= rec( Posa:= fail, Chvatal:= fail );
> repeat
> res:= CheckCriteriaOfPosaAndChvatal( classlengths, bounds );
> if result.Posa = fail and IsEmpty( res.badForPosa ) then
> result.Posa:= i;
> fi;
> if result.Chvatal = fail and IsEmpty( res.badForChvatal ) then
> result.Chvatal:= i;
> fi;
> i:= i+1;
> oldbounds:= bounds;
> bounds:= LowerBoundsVertexDegreesOfClosure( classlengths,
> bounds );
> until oldbounds = bounds;
>
> if result.Posa <> fail then
> if result.Posa <> result.Chvatal then
> return Concatenation(
> "Chvatal for ", Ordinal( result.Chvatal ), " closure, ",
> "Posa for ", Ordinal( result.Posa ), " closure" );
> else
> return Concatenation( "Posa for ", Ordinal( result.Posa ),
> " closure" );
> fi;
> elif result.Chvatal <> fail then
> return Concatenation( "Chvatal for ", Ordinal( result.Chvatal ),
> " closure" );
> else
> return "no decision";
> fi;
> end;;
## doc2/hamilcyc.xml (1221-1233)
gap> HamiltonianCycleInfoFromCharacterTable:= function( tbl )
> local prim, classlengths, bounds;
>
> prim:= PrimitivePermutationCharacters( tbl );
> if prim = fail then
> return "no prim. perm. characters";
> fi;
> classlengths:= SizesConjugacyClasses( tbl );
> bounds:= LowerBoundsVertexDegrees( classlengths, prim );
> return HamiltonianCycleInfo( classlengths, bounds );
> end;;
## doc2/hamilcyc.xml (1255-1267)
gap> spornames:= AllCharacterTableNames( IsSporadicSimple, true,
> IsDuplicateTable, false );
[ "B", "Co1", "Co2", "Co3", "F3+", "Fi22", "Fi23", "HN", "HS", "He",
"J1", "J2", "J3", "J4", "Ly", "M", "M11", "M12", "M22", "M23",
"M24", "McL", "ON", "Ru", "Suz", "Th" ]
gap> for tbl in List( spornames, CharacterTable ) do
> info:= HamiltonianCycleInfoFromCharacterTable( tbl );
> if info <> "Posa for 0th closure" then
> Print( Identifier( tbl ), ": ", info, "\n" );
> fi;
> od;
## doc2/hamilcyc.xml (1337-1344)
gap> dir:= DirectoriesPackageLibrary( "ctbllib", "data" );;
gap> filename:= Filename( dir, "prim_perm_M.json" );;
gap> primdata:= EvalString( StringFile( filename ) )[2];;
gap> Length( primdata );
46
gap> m:= CharacterTable( "M" );;
## doc2/hamilcyc.xml (1355-1368)
gap> s:= "dummy";; # Avoid a message about an unbound variable ...
gap> poss:= "dummy";; # Avoid a message about an unbound variable ...
gap> for entry in primdata do
> if not IsBound( entry[2] ) then
> s:= CharacterTable( entry[1] );
> poss:= Set( PossibleClassFusions( s, m ),
> x -> InducedClassFunctionsByFusionMap( s, m,
> [ TrivialCharacter( s ) ], x )[1] );
> entry[2]:= List( [ 1 .. NrConjugacyClasses( m ) ],
> i -> Maximum( List( poss, x -> x[i] ) ) );
> fi;
> od;
## doc2/hamilcyc.xml (1398-1402)
gap> prim:= List( primdata, x -> x[2] );;
gap> classlengths:= SizesConjugacyClasses( m );;
gap> bounds:= LowerBoundsVertexDegrees( classlengths, prim );;
## doc2/hamilcyc.xml (1414-1418)
gap> degs:= List( bounds, Sum );;
gap> Int( 100000000 * Minimum( degs ) / Size( m ) );
99999987
## doc2/hamilcyc.xml (1469-1506)
gap> PossibleClassFusions( CharacterTable( "U3(8).3_2" ), m );
[ ]
gap> badclasses:= [];;
gap> names:= [
> [ "L2(13)", "L2(13).2" ],
> [ "Sz(8)", "Sz(8).3" ],
> [ "U3(4)", "U3(4).2", "U3(4).4" ],
> [ "U3(8)", "U3(8).2", "U3(8).3_1", "U3(8).3_2", "U3(8).3_3",
> "U3(8).6" ],
> ];;
gap> for list in names do
> t:= CharacterTable( list[1] );
> tfusm:= PossibleClassFusions( t, m );
> UniteSet( badclasses, Flat( tfusm ) );
> for nam in list{ [ 2 .. Length( list ) ] } do
> ext:= CharacterTable( nam );
> for map1 in PossibleClassFusions( t, ext ) do
> inv:= InverseMap( map1 );
> for map2 in tfusm do
> init:= CompositionMaps( map2, inv );
> UniteSet( badclasses, Flat( PossibleClassFusions( ext, m,
> rec( fusionmap:= init ) ) ) );
> od;
> od;
> od;
> od;
gap> badclasses;
[ 1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 17, 18, 19, 20, 21, 22,
24, 25, 27, 28, 30, 32, 33, 35, 36, 38, 39, 40, 42, 43, 44, 45, 46,
48, 49, 50, 51, 52, 53, 54, 55, 56, 60, 61, 62, 63, 70, 72, 73, 78,
82, 85, 86 ]
gap> Length( badclasses );
55
gap> bad:= Sum( classlengths{ badclasses } ) / Size( m );;
gap> Int( 10000 * bad );
97
## doc2/hamilcyc.xml (1568-1577)
gap> prim:= List( primdata, x -> x[2] );;
gap> badpos:= Difference( badclasses, [ 1 ] ) - 1;;
gap> bounds:= LowerBoundsVertexDegrees( classlengths, prim );;
gap> for i in badpos do
> for j in badpos do
> bounds[i][j]:= 0;
> od;
> od;
## doc2/hamilcyc.xml (1605-1613)
gap> degs:= List( bounds, Sum );;
gap> Int( 10000 * Minimum( degs ) / Size( m ) );
9902
gap> goodpos:= Difference( [ 1 .. NrConjugacyClasses( m ) - 1 ],
> badpos );;
gap> Int( 100000000 * Minimum( degs{ goodpos } ) / Size( m ) );
99999987
## doc2/hamilcyc.xml (1630-1655)
gap> spornames:= AllCharacterTableNames( IsSporadicSimple, true,
> IsDuplicateTable, false );;
gap> sporautnames:= AllCharacterTableNames( IsSporadicSimple, true,
> IsDuplicateTable, false,
> OfThose, AutomorphismGroup );;
gap> sporautnames:= Difference( sporautnames, spornames );
[ "F3+.2", "Fi22.2", "HN.2", "HS.2", "He.2", "J2.2", "J3.2", "M12.2",
"M22.2", "McL.2", "ON.2", "Suz.2" ]
gap> for tbl in List( sporautnames, CharacterTable ) do
> info:= HamiltonianCycleInfoFromCharacterTable( tbl );
> Print( Identifier( tbl ), ": ", info, "\n" );
> od;
F3+.2: Chvatal for 0th closure, Posa for 1st closure
Fi22.2: Chvatal for 0th closure, Posa for 1st closure
HN.2: Chvatal for 0th closure, Posa for 1st closure
HS.2: Chvatal for 1st closure, Posa for 2nd closure
He.2: Chvatal for 0th closure, Posa for 1st closure
J2.2: Chvatal for 0th closure, Posa for 1st closure
J3.2: Chvatal for 0th closure, Posa for 1st closure
M12.2: Chvatal for 0th closure, Posa for 1st closure
M22.2: Posa for 1st closure
McL.2: Chvatal for 0th closure, Posa for 1st closure
ON.2: Chvatal for 0th closure, Posa for 1st closure
Suz.2: Chvatal for 0th closure, Posa for 1st closure
## doc2/hamilcyc.xml (1672-1680)
gap> for tbl in List( [ 5 .. 13 ], i -> CharacterTable(
> Concatenation( "A", String( i ) ) ) ) do
> info:= HamiltonianCycleInfoFromCharacterTable( tbl );
> if info <> "Posa for 0th closure" then
> Print( Identifier( tbl ), ": ", info, "\n" );
> fi;
> od;
## doc2/hamilcyc.xml (1689-1704)
gap> for tbl in List( [ 5 .. 13 ], i -> CharacterTable(
> Concatenation( "S", String( i ) ) ) ) do
> info:= HamiltonianCycleInfoFromCharacterTable( tbl );
> Print( Identifier( tbl ), ": ", info, "\n" );
> od;
A5.2: no decision
A6.2_1: Chvatal for 4th closure, Posa for 5th closure
A7.2: Posa for 1st closure
A8.2: Chvatal for 2nd closure, Posa for 3rd closure
A9.2: Chvatal for 2nd closure, Posa for 3rd closure
A10.2: Chvatal for 2nd closure, Posa for 3rd closure
A11.2: Posa for 1st closure
A12.2: Chvatal for 2nd closure, Posa for 3rd closure
A13.2: Posa for 1st closure
## doc2/hamilcyc.xml (1770-1785)
gap> HamiltonianCycleInfoFromGroup:= function( G )
> local ccl, nsg, der, degrees, classlengths;
> ccl:= ConjugacyClasses( G );
> if IsPerfect( G ) then
> nsg:= [];
> else
> der:= DerivedSubgroup( G );
> nsg:= Concatenation( [ der ],
> IntermediateSubgroups( G, der ).subgroups );
> fi;
> degrees:= VertexDegreesGeneratingGraph( G, ccl, nsg );
> classlengths:= List( ccl, Size );
> return HamiltonianCycleInfo( classlengths, degrees );
> end;;
## doc2/hamilcyc.xml (1797-1819)
gap> grps:= AllSmallNonabelianSimpleGroups( [ 1 .. 10^6 ] );;
gap> Length( grps );
56
gap> List( grps, StructureDescription );
[ "A5", "PSL(3,2)", "A6", "PSL(2,8)", "PSL(2,11)", "PSL(2,13)",
"PSL(2,17)", "A7", "PSL(2,19)", "PSL(2,16)", "PSL(3,3)",
"PSU(3,3)", "PSL(2,23)", "PSL(2,25)", "M11", "PSL(2,27)",
"PSL(2,29)", "PSL(2,31)", "A8", "PSL(3,4)", "PSL(2,37)", "O(5,3)",
"Sz(8)", "PSL(2,32)", "PSL(2,41)", "PSL(2,43)", "PSL(2,47)",
"PSL(2,49)", "PSU(3,4)", "PSL(2,53)", "M12", "PSL(2,59)",
"PSL(2,61)", "PSU(3,5)", "PSL(2,67)", "J1", "PSL(2,71)", "A9",
"PSL(2,73)", "PSL(2,79)", "PSL(2,64)", "PSL(2,81)", "PSL(2,83)",
"PSL(2,89)", "PSL(3,5)", "M22", "PSL(2,97)", "PSL(2,101)",
"PSL(2,103)", "HJ", "PSL(2,107)", "PSL(2,109)", "PSL(2,113)",
"PSL(2,121)", "PSL(2,125)", "O(5,4)" ]
gap> for g in grps do
> info:= HamiltonianCycleInfoFromGroup( g );
> if info <> "Posa for 0th closure" then
> Print( StructureDescription( g ), ": ", info, "\n" );
> fi;
> od;
## doc2/hamilcyc.xml (1957-1972)
gap> orders:= Filtered( [ 10^6+4, 10^6+8 .. 10^7 ],
> n -> IsomorphismTypeInfoFiniteSimpleGroup( n ) <> fail );
[ 1024128, 1123980, 1285608, 1342740, 1451520, 1653900, 1721400,
1814400, 1876896, 1934868, 2097024, 2165292, 2328648, 2413320,
2588772, 2867580, 2964780, 3265920, 3483840, 3594432, 3822588,
3940200, 4245696, 4680000, 4696860, 5515776, 5544672, 5663616,
5848428, 6004380, 6065280, 6324552, 6825840, 6998640, 7174332,
7906500, 8487168, 9095592, 9732420, 9951120, 9999360 ]
gap> Length( orders );
41
gap> info:= List( orders, IsomorphismTypeInfoFiniteSimpleGroup );;
gap> Number( info, x -> IsBound( x.series ) and x.series = "L"
> and x.parameter[1] = 2 );
31
## doc2/hamilcyc.xml (1987-2018)
gap> info:= Filtered( info, x -> not IsBound( x.series ) or
> x.series <> "L" or x.parameter[1] <> 2 );
[ rec( name := "B(3,2) = O(7,2) ~ C(3,2) = S(6,2)",
parameter := [ 3, 2 ], series := "B", shortname := "S6(2)" ),
rec( name := "A(10)", parameter := 10, series := "A",
shortname := "A10" ),
rec( name := "A(2,7) = L(3,7) ", parameter := [ 3, 7 ],
series := "L", shortname := "L3(7)" ),
rec( name := "2A(3,3) = U(4,3) ~ 2D(3,3) = O-(6,3)",
parameter := [ 3, 3 ], series := "2A", shortname := "U4(3)" ),
rec( name := "G(2,3)", parameter := 3, series := "G",
shortname := "G2(3)" ),
rec( name := "B(2,5) = O(5,5) ~ C(2,5) = S(4,5)",
parameter := [ 2, 5 ], series := "B", shortname := "S4(5)" ),
rec( name := "2A(2,8) = U(3,8)", parameter := [ 2, 8 ],
series := "2A", shortname := "U3(8)" ),
rec( name := "2A(2,7) = U(3,7)", parameter := [ 2, 7 ],
series := "2A", shortname := "U3(7)" ),
rec( name := "A(3,3) = L(4,3) ~ D(3,3) = O+(6,3) ",
parameter := [ 4, 3 ], series := "L", shortname := "L4(3)" ),
rec( name := "A(4,2) = L(5,2) ", parameter := [ 5, 2 ],
series := "L", shortname := "L5(2)" ) ]
gap> names:= [ "S6(2)", "A10", "L3(7)", "U4(3)", "G2(3)", "S4(5)",
> "U3(8)", "U3(7)", "L4(3)", "L5(2)" ];;
gap> for tbl in List( names, CharacterTable ) do
> info:= HamiltonianCycleInfoFromCharacterTable( tbl );
> if info <> "Posa for 0th closure" then
> Print( Identifier( tbl ), ": ", info, "\n" );
> fi;
> od;
## doc2/hamilcyc.xml (2049-2180)
gap> grps:= AllSmallNonabelianSimpleGroups( [ 1 .. 10^6 ] );;
gap> epi:= "dummy";; # Avoid a message about an unbound variable ...
gap> for simple in grps do
> for n in [ 1 .. LogInt( 10^6, Size( simple ) ) ] do
> # Compute the n-fold direct product S^n.
> soc:= CallFuncList( DirectProduct,
> ListWithIdenticalEntries( n, simple ) );
> # Compute Aut(S^n) as a permutation group.
> aut:= Image( IsomorphismPermGroup( AutomorphismGroup( soc ) ) );
> aut:= Image( SmallerDegreePermutationRepresentation( aut ) );
> # Compute class representatives of subgroups of
> # Aut(S^n)/Inn(S^n).
> socle:= Socle( aut );
> epi:= NaturalHomomorphismByNormalSubgroup( aut, socle );
> # Compute the candidates for G. (By the above computations,
> # we need not consider simple groups.)
> reps:= List( ConjugacyClassesSubgroups( Image( epi ) ),
> Representative );
> reps:= Filtered( reps, x -> IsCyclic( x ) and Size( x ) <> 1 );
> greps:= Filtered( List( reps, x -> PreImages( epi, x ) ),
> x -> Length( MinimalNormalSubgroups( x ) ) = 1 );
> for g in greps do
> # We have to deal with a *transitive* permutation group.
> # (Each group in question acts faithfully on an orbit.)
> if not IsTransitive( g ) then
> g:= First( List( Orbits( g, MovedPoints( g ) ),
> x -> Action( g, x ) ),
> x -> Size( x ) = Size( g ) );
> fi;
> # Check this group G.
> info:= HamiltonianCycleInfoFromGroup( g );
> Print( Name( simple ), "^", n, ".", Size( g ) / Size( soc ),
> ": ", info, "\n" );
> od;
> od;
> od;
A5^1.2: Posa for 2nd closure
A5^2.2: Posa for 0th closure
A5^2.4: Posa for 0th closure
A5^3.3: Posa for 0th closure
A5^3.6: Chvatal for 1st closure, Posa for 2nd closure
PSL(2,7)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,7)^2.2: Posa for 0th closure
PSL(2,7)^2.4: Posa for 0th closure
A6^1.2: Chvatal for 0th closure, Posa for 1st closure
A6^1.2: Chvatal for 4th closure, Posa for 5th closure
A6^1.2: Chvatal for 0th closure, Posa for 1st closure
A6^2.2: Posa for 0th closure
A6^2.4: Posa for 0th closure
A6^2.4: Posa for 0th closure
A6^2.4: Posa for 0th closure
PSL(2,8)^1.3: Posa for 0th closure
PSL(2,8)^2.2: Posa for 0th closure
PSL(2,8)^2.6: Chvatal for 0th closure, Posa for 1st closure
PSL(2,11)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,11)^2.2: Posa for 0th closure
PSL(2,11)^2.4: Posa for 0th closure
PSL(2,13)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,17)^1.2: Chvatal for 0th closure, Posa for 1st closure
A7^1.2: Posa for 1st closure
PSL(2,19)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,16)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,16)^1.4: Chvatal for 0th closure, Posa for 1st closure
PSL(3,3)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSU(3,3)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,23)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,25)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,25)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,25)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,27)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,27)^1.3: Posa for 0th closure
PSL(2,27)^1.6: Chvatal for 0th closure, Posa for 1st closure
PSL(2,29)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,31)^1.2: Chvatal for 0th closure, Posa for 1st closure
A8^1.2: Chvatal for 2nd closure, Posa for 3rd closure
PSL(3,4)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(3,4)^1.2: Chvatal for 1st closure, Posa for 2nd closure
PSL(3,4)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(3,4)^1.3: Posa for 0th closure
PSL(3,4)^1.6: Chvatal for 0th closure, Posa for 1st closure
PSL(2,37)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSp(4,3)^1.2: Chvatal for 1st closure, Posa for 2nd closure
Sz(8)^1.3: Posa for 0th closure
PSL(2,32)^1.5: Posa for 0th closure
PSL(2,41)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,43)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,47)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,49)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,49)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,49)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSU(3,4)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSU(3,4)^1.4: Chvatal for 0th closure, Posa for 1st closure
PSL(2,53)^1.2: Chvatal for 0th closure, Posa for 1st closure
M12^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,59)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,61)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSU(3,5)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSU(3,5)^1.3: Posa for 0th closure
PSL(2,67)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,71)^1.2: Chvatal for 0th closure, Posa for 1st closure
A9^1.2: Chvatal for 2nd closure, Posa for 3rd closure
PSL(2,73)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,79)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,64)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,64)^1.3: Posa for 0th closure
PSL(2,64)^1.6: Chvatal for 0th closure, Posa for 1st closure
PSL(2,81)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,81)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,81)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,81)^1.4: Chvatal for 0th closure, Posa for 1st closure
PSL(2,81)^1.4: Chvatal for 0th closure, Posa for 1st closure
PSL(2,83)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,89)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(3,5)^1.2: Chvatal for 0th closure, Posa for 1st closure
M22^1.2: Posa for 1st closure
PSL(2,97)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,101)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,103)^1.2: Chvatal for 0th closure, Posa for 1st closure
J_2^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,107)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,109)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,113)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,121)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,121)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,121)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,125)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSL(2,125)^1.3: Posa for 0th closure
PSL(2,125)^1.6: Chvatal for 0th closure, Posa for 1st closure
PSp(4,4)^1.2: Chvatal for 0th closure, Posa for 1st closure
PSp(4,4)^1.4: Posa for 0th closure
## doc2/hamilcyc.xml (2546-2574)
gap> TestL2q:= function( t )
> local name, orders, nccl, cl, prim, bds, n, ord;
>
> name:= Identifier( t );
> orders:= OrdersClassRepresentatives( t );
> nccl:= Length( orders );
> cl:= SizesConjugacyClasses( t );
> prim:= PrimitivePermutationCharacters( t );
> bds:= List( LowerBoundsVertexDegrees( cl, prim ), Sum );
> n:= List( [ 1 .. 5 ], i -> Sum( cl{ Filtered( [ 1 .. nccl ],
> x -> orders[x] = i ) } ) );
> if ForAny( Filtered( [ 1 .. nccl ], i -> orders[i] > 5 ),
> i -> bds[i-1] <= Size( t ) / 2 ) then
> Error( "problem with large orders for ", name );
> elif ForAny( Filtered( [ 1 .. nccl ], i -> orders[i] = 2 ),
> i -> bds[i-1] <= n[2] ) then
> Error( "problem with order 2 for ", name, "\n" );
> elif ForAny( Filtered( [ 1 .. nccl ],
> i -> orders[i] in [ 3 .. 5 ] ),
> i -> bds[i-1] <= Sum( n{ [ 2 .. 5 ] } ) ) then
> Error( "problem with order in [ 3 .. 5 ] for ", name );
> fi;
> end;;
gap> for q in Filtered( [ 13 .. 59 ], IsPrimePowerInt ) do
> TestL2q( CharacterTable(
> Concatenation( "L2(", String( q ), ")" ) ) );
> od;
## doc2/hamilcyc.xml (2584-2591)
gap> for q in Filtered( [ 2 .. 11 ], IsPrimePowerInt ) do
> info:= HamiltonianCycleInfoFromGroup( PSL( 2, q ) );
> if info <> "Posa for 0th closure" then
> Print( q, ": ", info, "\n" );
> fi;
> od;
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> data.replayInterval:= oldinterval;
> fi;
##
gap> STOP_TEST( "hamilcyc.tst" );
gap> SizeScreen( save );;
#############################################################################
##
#E
