Quelle maintain.tst
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# This file was created automatically, do not edit!
#############################################################################
##
#W maintain.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( "maintain.tst" );'.
##
gap> LoadPackage( "CTblLib", false );
true
gap> save:= SizeScreen();;
gap> SizeScreen( [ 72 ] );;
gap> START_TEST( "maintain.tst" );
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> oldinterval:= data.replayInterval;
> data.replayInterval:= 1;
> fi;
## doc2/maintain.xml (71-99)
gap> tbl:= rec(
> Identifier:= "P41/G1/L1/V4/ext2",
> InfoText:= Concatenation( [
> "origin: Hanrath library,\n",
> "structure is 2^7.L2(8),\n",
> "characters sorted with permutation (12,14,15,13)(19,20)" ] ),
> UnderlyingCharacteristic:= 0,
> SizesCentralizers:= [64512,1024,1024,64512,64,64,64,64,128,128,64,
> 64,128,128,18,18,14,14,14,14,14,14,18,18,18,18,18,18],
> ComputedPowerMaps:= [,[1,1,1,1,2,3,3,2,3,2,2,1,3,2,16,16,20,20,22,
> 22,18,18,26,26,27,27,23,23],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,4,
> 1,21,22,17,18,19,20,16,15,15,16,16,15],,,,[1,2,3,4,5,6,7,8,9,10,
> 11,12,13,14,15,16,4,1,4,1,4,1,26,25,28,27,23,24]],
> Irr:= 0,
> AutomorphismsOfTable:= Group( [(23,26,27)(24,25,28),(9,13)(10,14),
> (17,19,21)(18,20,22)] ),
> ConstructionInfoCharacterTable:= ["ConstructClifford",[[[1,2,3,4,
> 5,6,7,8,9],[1,7,8,3,9,2],[1,4,5,6,2],[1,2,2,2,2,2,2,2]],
> [["L2(8)"],["Dihedral",18],["Dihedral",14],["2^3"]],[[[1,2,3,4],
> [1,1,1,1],["elab",4,25]],[[1,2,3,4,4,4,4,4,4,4],[2,6,5,2,3,4,5,
> 6,7,8],["elab",10,17]],[[1,2],[3,4],[[1,1],[-1,1]]],[[1,3],[4,
> 2],[[1,1],[-1,1]]],[[1,3],[5,3],[[1,1],[-1,1]]],[[1,3],[6,4],
> [[1,1],[-1,1]]],[[1,2],[7,2],[[1,1],[1,-1]]],[[1,2],[8,3],[[1,
> 1],[-1,1]]],[[1,2],[9,5],[[1,1],[1,-1]]]]]],
> );;
gap> ConstructClifford( tbl, tbl.ConstructionInfoCharacterTable[2] );
gap> ConvertToLibraryCharacterTableNC( tbl );;
## doc2/maintain.xml (108-113)
gap> Length( LinearCharacters( tbl ) );
1
gap> IsPerfectCharacterTable( tbl );
true
## doc2/maintain.xml (124-138)
gap> IsInternallyConsistent( tbl );
true
gap> irr:= Irr( tbl );;
gap> test:= Concatenation( List( [ 2 .. 7 ],
> n -> Symmetrizations( tbl, irr, n ) ) );;
gap> Append( test, Set( Tensored( irr, irr ) ) );
gap> fail in Decomposition( irr, test, "nonnegative" );
false
gap> if ForAny( Tuples( [ 1 .. NrConjugacyClasses( tbl ) ], 3 ),
> t -> not ClassMultiplicationCoefficient( tbl, t[1], t[2], t[3] )
> in NonnegativeIntegers ) then
> Error( "contradiction" );
> fi;
## doc2/maintain.xml (147-155)
gap> n:= Size( tbl );
64512
gap> NumberPerfectGroups( n );
4
gap> grps:= List( [ 1 .. 4 ], i -> PerfectGroup( IsPermGroup, n, i ) );
[ L2(8) 2^6 E 2^1, L2(8) N 2^6 E 2^1 I, L2(8) N 2^6 E 2^1 II,
L2(8) N 2^6 E 2^1 III ]
## doc2/maintain.xml (165-170)
gap> tbls:= List( grps, CharacterTable );;
gap> List( tbls,
> x -> TransformingPermutationsCharacterTables( x, tbl ) );
[ fail, fail, fail, fail ]
## doc2/maintain.xml (179-183)
gap> List( tbls,
> t -> TransformingPermutations( Irr( t ), Irr( tbl ) ) );
[ fail, fail, fail, fail ]
## doc2/maintain.xml (195-203)
gap> testchars:= List( tbls,
> t -> Filtered( Irr( t ),
> x -> x[1] = 63 and Set( x ) = [ -1, 0, 7, 63 ] ) );;
gap> List( testchars, Length );
[ 1, 1, 1, 1 ]
gap> List( testchars, l -> Number( l[1], x -> x = 7 ) );
[ 2, 2, 2, 2 ]
## doc2/maintain.xml (223-231)
gap> testchars:= List( [ tbl ],
> t -> Filtered( Irr( t ),
> x -> x[1] = 63 and Set( x ) = [ -1, 0, 7, 63 ] ) );;
gap> List( testchars, Length );
[ 1 ]
gap> List( testchars, l -> Number( l[1], x -> x = 7 ) );
[ 1 ]
## doc2/maintain.xml (256-267)
gap> Filtered( [ 1 .. 4 ], i ->
> TransformingPermutationsCharacterTables( tbls[i],
> CharacterTable( "P41/G1/L1/V1/ext2" ) ) <> fail );
[ 1 ]
gap> Filtered( [ 1 .. 4 ], i ->
> TransformingPermutationsCharacterTables( tbls[i],
> CharacterTable( "P41/G1/L1/V2/ext2" ) ) <> fail );
[ 3 ]
gap> TransformingPermutations( Irr( tbls[1] ), Irr( tbls[3] ) ) <> fail;
true
## doc2/maintain.xml (283-290)
gap> Filtered( [ 1 .. 4 ], i ->
> TransformingPermutationsCharacterTables( tbls[i],
> CharacterTable( "P41/G1/L1/V4/ext2" ) ) <> fail );
[ 4 ]
gap> TransformingPermutations( Irr( tbls[2] ), Irr( tbls[4] ) ) <> fail;
true
## doc2/maintain.xml (432-437)
gap> g:= AtlasGroup( "E6(2)" );;
gap> repeat x:= PseudoRandom( g ); until Order( x ) = 91;
gap> CharacteristicPolynomial( x ) = CharacteristicPolynomial( x^11 );
false
## doc2/maintain.xml (446-452)
gap> t:= CharacterTable( "E6(2)" );;
gap> ord91:= Positions( OrdersClassRepresentatives( t ), 91 );
[ 163, 164, 165, 166, 167, 168 ]
gap> PowerMap( t, 11 ){ ord91 };
[ 167, 168, 163, 164, 165, 166 ]
## doc2/maintain.xml (490-525)
gap> t:= CharacterTable( "2.F4(2).2" );;
gap> f:= CharacterTable( "F4(2).2" );;
gap> map:= PowerMap( t, 2 );
[ 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 11, 11, 3, 3, 3, 5, 5, 5, 3, 6, 6, 5,
5, 7, 7, 5, 8, 7, 29, 29, 9, 9, 9, 9, 11, 11, 9, 9, 9, 9, 11, 11,
43, 43, 20, 20, 20, 14, 14, 13, 13, 20, 21, 24, 28, 28, 57, 57, 29,
29, 29, 29, 33, 33, 35, 37, 37, 37, 37, 33, 33, 37, 37, 35, 41, 41,
42, 42, 79, 79, 43, 43, 83, 83, 45, 45, 47, 47, 53, 53, 91, 91, 57,
57, 61, 61, 61, 98, 98, 70, 70, 63, 63, 81, 81, 83, 83, 1, 6, 7,
11, 16, 17, 24, 24, 21, 27, 27, 25, 26, 29, 41, 53, 53, 53, 46, 56,
56, 56, 56, 62, 75, 75, 78, 78, 77, 77, 79, 79, 86, 86, 85, 85, 88,
88, 88, 88, 95, 95, 96, 96 ]
gap> PositionSublist( map, [ 86, 86, 85, 85 ] );
140
gap> OrdersClassRepresentatives( t ){ [ 140 .. 143 ] };
[ 32, 32, 32, 32 ]
gap> SizesCentralizers( t ){ [ 140 .. 143 ] };
[ 64, 64, 64, 64 ]
gap> GetFusionMap( t, f ){ [ 140 ..143 ] };
[ 86, 86, 87, 87 ]
gap> PowerMap( f, 2 ){ [ 86, 87 ] };
[ 50, 50 ]
gap> pos:= PositionsProperty( Irr( t ),
> x -> x[1] <> x[2] and Length( Set( x{ [ 140 .. 143 ] } ) ) > 1 );
[ 144, 145, 146, 147 ]
gap> List( pos, i -> Irr(t)[i]{ [ 140 .. 143 ] } );
[ [ 2*E(16)-2*E(16)^7, -2*E(16)+2*E(16)^7, 2*E(16)^3-2*E(16)^5,
-2*E(16)^3+2*E(16)^5 ],
[ -2*E(16)+2*E(16)^7, 2*E(16)-2*E(16)^7, -2*E(16)^3+2*E(16)^5,
2*E(16)^3-2*E(16)^5 ],
[ -2*E(16)^3+2*E(16)^5, 2*E(16)^3-2*E(16)^5, 2*E(16)-2*E(16)^7,
-2*E(16)+2*E(16)^7 ],
[ 2*E(16)^3-2*E(16)^5, -2*E(16)^3+2*E(16)^5, -2*E(16)+2*E(16)^7,
2*E(16)-2*E(16)^7 ] ]
## doc2/maintain.xml (561-568)
gap> tbl:= CharacterTable( "Ly" );;
gap> orders:= OrdersClassRepresentatives( tbl );;
gap> order8:= Filtered( [ 1 .. Length( orders ) ], x -> orders[x] = 8 );
[ 12, 13 ]
gap> SizesCentralizers( tbl ){ order8 } / 2^6;
[ 15/2, 3/2 ]
## doc2/maintain.xml (586-593)
gap> g:= AtlasGroup( "McL.2" );;
gap> NrMovedPoints( g );
275
gap> syl:= SylowSubgroup( g, 2 );;
gap> pc:= Image( IsomorphismPcGroup( syl ) );;
gap> t:= CharacterTable( pc );;
## doc2/maintain.xml (602-606)
gap> IsRecord( TransformingPermutationsCharacterTables( t,
> CharacterTable( "LyN2" ) ) );
true
## doc2/maintain.xml (646-650)
gap> GroupInfoForCharacterTable( "A5" );;
gap> IsBound( CTblLib.FactorGroupOfPerfectSpaceGroup );
true
## doc2/maintain.xml (836-852)
gap> generatorsOfPerfectSpaceGroup:= function( Pgens, V, t )
> local d, result, i, m;
> d:= Length( Pgens[1] );
> result:= [];
> for i in [ 1 .. Length( Pgens ) ] do
> m:= IdentityMat( d+1 );
> m{ [ 1 .. d ] }{ [ 1 .. d ] }:= Pgens[i];
> m[ d+1 ]{ [ 1 .. d ] }:= V[i];
> result[i]:= m;
> od;
> m:= IdentityMat( d+1 );
> m[ d+1 ]{ [ 1 .. d ] }:= t;
> Add( result, m );
> return result;
> end;;
## doc2/maintain.xml (876-879)
gap> multiplicationModulo:= n -> function( v, g )
> return List( v * g, x -> x mod n ); end;;
## doc2/maintain.xml (892-905)
gap> deletedPermutationMat:= function( pi, n )
> local mat, j, i;
> mat:= PermutationMat( pi, n );
> mat:= mat{ [ 1 .. n-1 ] }{ [ 1 .. n-1 ] };
> j:= n ^ pi;
> if j <> n then
> for i in [ 1 .. n-1 ] do
> mat[i][j]:= -1;
> od;
> fi;
> return mat;
> end;;
## doc2/maintain.xml (962-982)
gap> verifyFactorGroup:= function( gens, id )
> local sm, act, stored, hom;
> sm:= SmallerDegreePermutationRepresentation( Group( gens ) );
> gens:= List( gens, x -> x^sm );
> act:= Images( sm );
> if not IsRecord( TransformingPermutationsCharacterTables(
> CharacterTable( act ),
> CharacterTable( id ) ) ) then
> return "wrong character table";
> fi;
> GroupInfoForCharacterTable( id );
> stored:= CTblLib.FactorGroupOfPerfectSpaceGroup( id );
> hom:= GroupHomomorphismByImages( stored, act,
> GeneratorsOfGroup( stored ), gens );
> if hom = fail or not IsBijective( hom ) then
> return "wrong group";
> fi;
> return true;
> end;;
## doc2/maintain.xml (997-1000)
gap> a:= deletedPermutationMat( (1,3)(2,4), 6 );;
gap> b:= deletedPermutationMat( (1,2,3)(4,5,6), 6 );;
## doc2/maintain.xml (1008-1010)
gap> v:= [ [ 2, 2, 0, 0, 1 ], 0 * b[1] ];;
## doc2/maintain.xml (1020-1022)
gap> t:= [ 2, 0, 0, 0, 0 ];;
## doc2/maintain.xml (1032-1040)
gap> sgens:= generatorsOfPerfectSpaceGroup( [ a, b ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 8 );;
gap> orb:= Orbit( g, [ 1, 0, 0, 0, 0, 1 ], fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P1/G2/L1/V2/ext4" );
true
## doc2/maintain.xml (1050-1056)
gap> bas:= [ [-1,-1, 1, 1, 1 ],
> [-1, 1,-1, 1, 1 ],
> [ 1, 1, 1,-1,-1 ],
> [ 1, 1,-1,-1, 1 ],
> [-1, 1, 1,-1, 1 ] ];;
## doc2/maintain.xml (1065-1071)
gap> B:= Basis( Rationals^Length( bas ), bas );;
gap> abas:= List( bas, x -> Coefficients( B, x * a ) );;
gap> bbas:= List( bas, x -> Coefficients( B, x * b ) );;
gap> vbas:= List( v, x -> Coefficients( B, x ) );
[ [ 3/2, 1, 2, 3/2, -1 ], [ 0, 0, 0, 0, 0 ] ]
## doc2/maintain.xml (1081-1086)
gap> vbas:= vbas * 2;
[ [ 3, 2, 4, 3, -2 ], [ 0, 0, 0, 0, 0 ] ]
gap> t:= 2 * t;
[ 4, 0, 0, 0, 0 ]
## doc2/maintain.xml (1098-1106)
gap> sgens:= generatorsOfPerfectSpaceGroup( [ abas, bbas ], vbas, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 16 );;
gap> orb:= Orbit( g, [ 0, 0, 0, 0, 0, 1 ], fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P1/G2/L2/V2/ext4" );
true
## doc2/maintain.xml (1122-1135)
gap> a:= [ [ 0, 1, 0, 1, 0, 0 ],
> [ 1, 0, 1, 1, 1, 1 ],
> [-1,-1,-1,-1, 0, 0 ],
> [ 0, 0,-1,-1,-1,-1 ],
> [ 1, 1, 1, 1, 0, 1 ],
> [ 0, 0, 1, 0, 1, 0 ] ];;
gap> b:= [ [-1, 0, 0, 0, 0,-1 ],
> [ 0, 0,-1, 0,-1, 0 ],
> [ 1, 1, 1, 1, 1, 1 ],
> [ 0, 0, 1, 0, 0, 0 ],
> [-1,-1,-1, 0, 0, 0 ],
> [ 1, 0, 0, 0, 0, 0 ] ];;
## doc2/maintain.xml (1152-1163)
gap> v:= List( [ 1, 2 ], i -> 0 * a[1] );;
gap> t:= [ 1, 0, 0, 0, 0, 0 ];;
gap> sgens:= generatorsOfPerfectSpaceGroup( [ a, b ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 4 );;
gap> seed:= [ 1, 0, 0, 0, 0, 0, 1 ];;
gap> orb:= Orbit( g, seed, fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P11/G1/L1/V1/ext4" );
true
## doc2/maintain.xml (1178-1188)
gap> v:= [ [ 1, 0, 1, 0, 0, 0 ], 0 * a[1] ];;
gap> t:= [ 2, 0, 0, 0, 0, 0 ];;
gap> sgens:= generatorsOfPerfectSpaceGroup( [ a, b ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 8 );;
gap> orb:= Orbit( g, [ 1, 0, 0, 0, 0, 0, 1 ], fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P11/G1/L1/V2/ext4" );
true
## doc2/maintain.xml (1203-1213)
gap> v:= [ [ 0, 1, 0, 0, 1, 0 ], 0 * a[1] ];;
gap> t:= [ 2, 0, 0, 0, 0, 0 ];;
gap> sgens:= generatorsOfPerfectSpaceGroup( [ a, b ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 8 );;
gap> orb:= Orbit( g, [ 1, 0, 0, 0, 0, 0, 1 ], fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P11/G1/L1/V3/ext4" );
true
## doc2/maintain.xml (1222-1239)
gap> a:= [ [ 1, 0, 0, 1, 0,-1, 0, 1 ],
> [ 0,-1, 1, 0,-1, 0, 0, 0 ],
> [ 1, 0, 0, 1, 0,-1, 0, 0 ],
> [ 0,-1, 0,-1, 0, 1, 1,-1 ],
> [ 1, 0,-1, 1, 1,-1, 0, 0 ],
> [ 1,-1,-1, 0, 0, 0, 1, 0 ],
> [ 0,-1, 1, 0,-1, 1, 0,-1 ],
> [ 1, 0,-1, 0, 0, 0, 0, 0 ] ];;
gap> b:= [ [ 1, 0,-2, 0, 1,-1, 1, 0 ],
> [ 0,-1, 0, 0, 0, 0, 1,-1 ],
> [ 1, 0,-1, 0, 1,-1, 0, 0 ],
> [-1,-1, 1,-1,-1, 2, 0,-1 ],
> [ 0, 0, 0,-1, 0, 0, 0, 0 ],
> [ 0,-1, 0,-1,-1, 1, 1,-1 ],
> [ 1,-1, 0, 0, 0, 0, 0, 0 ],
> [ 1, 0, 0, 0, 0, 0, 0, 0 ] ];;
## doc2/maintain.xml (1254-1265)
gap> v:= List( [ 1, 2 ], i -> 0 * a[1] );;
gap> t:= [ 1, 0, 0, 0, 0, 0, 0, 0 ];;
gap> sgens:= generatorsOfPerfectSpaceGroup( [ a, b ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 3 );;
gap> seed:= [ 1, 0, 0, 0, 0, 0, 0, 0, 1 ];;
gap> orb:= Orbit( g, seed, fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P11/G4/L1/V1/ext3" );
true
## doc2/maintain.xml (1280-1290)
gap> a:= KroneckerProduct( IdentityMat( 4 ), [ [ 0, 1 ], [ -1, 0 ] ] );;
gap> b:= [ [ 0,-1, 0, 0, 0, 0, 0, 0 ],
> [ 0, 0, 1, 0, 0, 0, 0, 0 ],
> [-1, 0, 0, 0, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 0,-1, 0 ],
> [ 0, 0, 0,-1, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 1, 0, 0 ],
> [ 0, 0, 0, 0, 1, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 0, 0, 1 ] ];;
## doc2/maintain.xml (1301-1310)
gap> bas:= [ [ 1, 1, 0, 0, 0, 0, 0, 0 ],
> [ 0, 1, 1, 0, 0, 0, 0, 0 ],
> [ 0, 0, 1, 1, 0, 0, 0, 0 ],
> [ 0, 0, 0, 1, 1, 0, 0, 0 ],
> [ 0, 0, 0, 0, 1, 1, 0, 0 ],
> [ 0, 0, 0, 0, 0, 1, 1, 0 ],
> [ 0, 0, 0, 0, 0, 0, 1, 1 ],
> [ 0, 0, 0, 0, 0, 0,-1, 1 ] ];;
## doc2/maintain.xml (1318-1322)
gap> B:= Basis( Rationals^Length( bas ), bas );;
gap> abas:= List( bas, x -> Coefficients( B, x * a ) );;
gap> bbas:= List( bas, x -> Coefficients( B, x * b ) );;
## doc2/maintain.xml (1337-1352)
gap> v:= List( [ 1, 2 ], i -> 0 * a[1] );;
gap> t:= [ 1, 0, 0, 0, 0, 0, 0, 0 ];;
gap> sgens:= generatorsOfPerfectSpaceGroup( [ abas, bbas ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 2 );;
gap> funpairs:= function( pair, g )
> return [ fun( pair[1], g ), pair[2] * g ];
> end;;
gap> seed:= [ [ 1, 0, 0, 0, 0, 0, 0, 0, 1 ],
> [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ];;
gap> orb:= Orbit( g, seed, funpairs );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, funpairs ) );;
gap> verifyFactorGroup( permgens, "P12/G1/L2/V1/ext2" );
true
## doc2/maintain.xml (1367-1371)
gap> a:= PermutationMat( (2,4)(5,7), 7 );;
gap> b:= PermutationMat( (1,3,2)(4,6,5), 7 );;
gap> c:= DiagonalMat( [ -1, -1, 1, 1, -1, -1, 1 ] );;
## doc2/maintain.xml (1382-1390)
gap> bas:= [ [ 1, 1, 0, 0, 0, 0, 0 ],
> [ 0, 1, 1, 0, 0, 0, 0 ],
> [ 0, 0, 1, 1, 0, 0, 0 ],
> [ 0, 0, 0, 1, 1, 0, 0 ],
> [ 0, 0, 0, 0, 1, 1, 0 ],
> [ 0, 0, 0, 0, 0, 1, 1 ],
> [ 0, 0, 0, 0, 0,-1, 1 ] ];;
## doc2/maintain.xml (1398-1403)
gap> B:= Basis( Rationals^Length( bas ), bas );;
gap> abas:= List( bas, x -> Coefficients( B, x * a ) );;
gap> bbas:= List( bas, x -> Coefficients( B, x * b ) );;
gap> cbas:= List( bas, x -> Coefficients( B, x * c ) );;
## doc2/maintain.xml (1413-1424)
gap> v:= List( [ 1 .. 3 ], i -> 0 * a[1] );;
gap> t:= [ 1, 0, 0, 0, 0, 0, 0 ];;
gap> sgens:= generatorsOfPerfectSpaceGroup( [ abas,bbas,cbas ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 2 );;
gap> orb:= Orbit( g, [ 1, 0, 0, 0, 0, 0, 0, 1 ], fun );;
gap> act:= Action( g, orb, fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P13/G1/L2/V1/ext2" );
true
## doc2/maintain.xml (1439-1460)
gap> b:= [ [ 0,-1, 0, 0, 0, 0, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0,-1, 0, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
> [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
> [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
> [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
> [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ];;
gap> c:= [ [ 0, 0, 0, 0, 0, 0, 0,-1, 0, 0 ],
> [ 0, 0, 0, 0, 0, 0, 0,-1, 1,-1 ],
> [ 0, 0, 0, 0,-1, 1, 0,-1, 0, 0 ],
> [ 0,-1, 1, 0, 0, 0, 0,-1, 0, 0 ],
> [ 0, 0, 0, 0, 0, 0, 0, 0, 0,-1 ],
> [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
> [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 1,-1, 0, 0, 1 ],
> [ 0, 0, 1,-1, 0, 0, 0, 0, 0, 1 ],
> [-1, 0, 1, 0, 0,-1, 0, 0, 0, 0 ] ];;
## doc2/maintain.xml (1470-1491)
gap> bas2:= [ [ 0, 1,-1, 0, 0, 0, 0, 0, 0, 0 ],
> [ 0, 0, 1,-1, 0, 0, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 1,-1, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 1,-1, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 1, 0,-1, 0, 0 ],
> [ 0, 0, 0, 0, 0, 0, 0, 1,-1, 0 ],
> [ 0, 0, 0, 0, 0, 0, 0, 0, 1,-1 ],
> [ 0, 0, 0, 1, 0, 0, 0, 0, 0,-1 ],
> [ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0 ],
> [ 1, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ];;
gap> bas5:= [ [ 0,-1, 1, 1,-1, 1, 1,-1,-1, 0 ],
> [ 1, 0,-1,-1,-1, 1, 1,-1,-1, 0 ],
> [ 0, 1, 1,-1, 1, 1,-1, 0, 1, 1 ],
> [ 1, 1, 0,-1, 0,-1, 1,-1, 1,-1 ],
> [-1, 0,-1, 1, 1, 0,-1,-1, 1,-1 ],
> [ 0, 1,-1, 1, 1,-1, 1, 1, 0,-1 ],
> [-1,-1, 1, 1, 0,-1,-1,-1,-1, 0 ],
> [ 1,-1, 0,-1, 1,-1, 1, 1, 0,-1 ],
> [-1, 1,-1, 1,-1, 0,-1, 1, 0,-1 ],
> [ 1,-1,-1, 1, 1, 1, 0, 0,-1,-1 ] ];;
## doc2/maintain.xml (1500-1507)
gap> B2:= Basis( Rationals^Length( bas2 ), bas2 );;
gap> bbas2:= List( bas2, x -> Coefficients( B2, x * b ) );;
gap> cbas2:= List( bas2, x -> Coefficients( B2, x * c ) );;
gap> B5:= Basis( Rationals^Length( bas5 ), bas5 );;
gap> bbas5:= List( bas5, x -> Coefficients( B5, x * b ) );;
gap> cbas5:= List( bas5, x -> Coefficients( B5, x * c ) );;
## doc2/maintain.xml (1517-1528)
gap> v:= List( [ 1, 2 ], i -> 0 * bbas2[1] );;
gap> t:= [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ];;
gap> sgens:= generatorsOfPerfectSpaceGroup( [ bbas2, cbas2 ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 2 );;
gap> seed:= [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ];;
gap> orb:= Orbit( g, seed, fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P21/G3/L2/V1/ext2" );
true
## doc2/maintain.xml (1538-1545)
gap> sgens:= generatorsOfPerfectSpaceGroup( [ bbas5, cbas5 ], v, t );;
gap> g:= Group( sgens );;
gap> orb:= Orbit( g, seed, fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P21/G3/L5/V1/ext2" );
true
## doc2/maintain.xml (1560-1575)
gap> a:= [ [ 0,-1, 0, 1, 0,-1, 1],
> [ 0, 0,-1, 0, 1,-1, 0],
> [ 0, 0, 0,-1, 1, 0, 0],
> [ 0, 0, 0,-1, 0, 0, 0],
> [ 0, 0, 1,-1, 0, 0, 0],
> [ 0,-1, 1, 0,-1, 0, 0],
> [ 1,-1, 0, 1, 0,-1, 0] ];;
gap> b:= [ [-1, 0, 1, 0,-1, 1, 0],
> [ 0,-1, 0, 1,-1, 0, 0],
> [ 0, 0,-1, 1, 0, 0, 0],
> [ 0, 0,-1, 0, 0, 0, 0],
> [ 0, 1,-1, 0, 0, 0, 0],
> [-1, 1, 0,-1, 0, 0, 0],
> [-1, 0, 1, 0,-1, 0, 1] ];;
## doc2/maintain.xml (1584-1588)
gap> v:= [ [ 2, 1, 0, 0, 0, 1, 4 ],
> [ 2, 0, 0, 0, 0, 0, 0 ] ];;
gap> t:= [ 3, 0, 0, 0, 0, 0, 0 ];;
## doc2/maintain.xml (1603-1620)
gap> sgens:= generatorsOfPerfectSpaceGroup( [ a, b ], v, t );;
gap> g:= Group( sgens );;
gap> aa:= sgens[1];;
gap> bb:= sgens[2];;
gap> elm:= aa*bb;;
gap> Order( elm );
7
gap> fixed:= NullspaceMat( elm - aa^0 );
[ [ 1, 1, 1, 1, 1, 1, 1, 0 ], [ -4, 1, 1, -5, -5, 2, 0, 1 ] ]
gap> fun:= multiplicationModulo( 9 );;
gap> seed:= fun( fixed[2], aa^0 );
[ 5, 1, 1, 4, 4, 2, 0, 1 ]
gap> orb:= Orbit( g, seed, fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P41/G1/L1/V3/ext3" );
true
## doc2/maintain.xml (1629-1631)
gap> t:= [ 6, 0, 0, 0, 0, 0, 0 ];;
## doc2/maintain.xml (1641-1651)
gap> fun:= multiplicationModulo( 18 );;
gap> sgens:= generatorsOfPerfectSpaceGroup( [ a, b ], v, t );;
gap> g:= Group( sgens );;
gap> seed:= fun( fixed[2], aa^0 );
[ 14, 1, 1, 13, 13, 2, 0, 1 ]
gap> orb:= Orbit( g, seed, fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P41/G1/L1/V4/ext3" );
true
## doc2/maintain.xml (1666-1669)
gap> a:= deletedPermutationMat( (1,9)(3,5)(7,11)(8,10), 11 );;
gap> b:= deletedPermutationMat( (1,4,3,2)(5,8,7,6), 11 );;
## doc2/maintain.xml (1678-1682)
gap> v:= [ 0 * a[1],
> [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ] ];;
gap> t:= [ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 ];;
## doc2/maintain.xml (1692-1700)
gap> sgens:= generatorsOfPerfectSpaceGroup( [ a, b ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 4 );;
gap> orb:= Orbit( g, [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ], fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P48/G1/L1/V2/ext2" );
true
## doc2/maintain.xml (1715-1730)
gap> a:= [ [ 0, 0,-1, 1, 0,-1, 1 ],
> [ 1, 0,-1, 1, 1,-1, 0 ],
> [ 0, 1,-1, 0, 1, 0,-1 ],
> [ 0, 1, 0,-1, 1, 0,-1 ],
> [-1, 1, 1,-1, 0, 1, 0 ],
> [-1, 0, 1,-1, 0, 0, 1 ],
> [ 0, 0, 0, 0, 0, 0, 1 ] ];;
gap> b:= [ [ 0, 0, 0, 0, 0, 0, 1 ],
> [ 0, 0,-1, 1, 0,-1, 1 ],
> [ 1, 0,-1, 1, 1,-1, 0 ],
> [ 0, 1,-1, 0, 1, 0,-1 ],
> [ 0, 1, 0,-1, 1, 0,-1 ],
> [-1, 1, 1,-1, 0, 1, 0 ],
> [-1, 0, 1,-1, 0, 0, 1 ] ];;
## doc2/maintain.xml (1739-1743)
gap> v:= [ [ 2, 1, 0, 0, 2, 1, 0 ],
> 0 * b[1] ];;
gap> t:= [ 3, 0, 0, 0, 0, 0, 0 ];;
## doc2/maintain.xml (1753-1757)
gap> sgens:= generatorsOfPerfectSpaceGroup( [ a, b ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 9 );;
## doc2/maintain.xml (1766-1780)
gap> aa:= sgens[1];;
gap> bb:= sgens[2];;
gap> elm:= aa*bb^4;;
gap> Order( elm );
12
gap> fixed:= NullspaceMat( elm - aa^0 );
[ [ -1, -1, 1, 1, -1, -1, 1, 0 ], [ 0, -3, 1, 1, -1, -2, 0, 1 ] ]
gap> seed:= fun( fixed[2], aa^0 );
[ 0, 6, 1, 1, 8, 7, 0, 1 ]
gap> orb:= Orbit( g, seed, fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P49/G1/L1/V2/ext3" );
true
## doc2/maintain.xml (1795-1808)
gap> a:= [ [ 0, 1, 0,-1,-1, 1 ],
> [ 1, 0,-1, 0, 1, 0 ],
> [ 0, 0, 0,-1, 0, 1 ],
> [ 0, 0,-1, 0, 0, 1 ],
> [ 0, 0, 0, 0, 1, 0 ],
> [ 0, 0, 0, 0, 0, 1 ] ];;
gap> b:= [ [ 0,-1, 0, 1, 0,-1 ],
> [ 0, 1, 0,-1,-1, 0 ],
> [ 0, 0, 1, 1, 0,-1 ],
> [ 0, 0, 0, 0,-1, 0 ],
> [ 0, 1, 0, 0, 0, 0 ],
> [ 1, 0, 0, 0, 0, 0 ] ];;
## doc2/maintain.xml (1817-1820)
gap> v:= List( [ 1, 2 ], i -> 0 * a[1] );;
gap> t:= [ 1, 0, 0, 0, 0, 0 ];;
## doc2/maintain.xml (1830-1838)
gap> sgens:= generatorsOfPerfectSpaceGroup( [ a, b ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 3 );;
gap> orb:= Orbit( g, [ 1, 0, 0, 0, 0, 0, 1 ], fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P50/G1/L1/V1/ext3" );
true
## doc2/maintain.xml (1848-1856)
gap> sgens:= generatorsOfPerfectSpaceGroup( [ a, b ], v, t );;
gap> g:= Group( sgens );;
gap> fun:= multiplicationModulo( 4 );;
gap> orb:= Orbit( g, [ 1, 0, 0, 0, 0, 0, 1 ], fun );;
gap> permgens:= List( sgens, x -> Permutation( x, orb, fun ) );;
gap> verifyFactorGroup( permgens, "P50/G1/L1/V1/ext4" );
true
## doc2/maintain.xml (1871-1877)
gap> degrees:= CharacterDegrees( CharacterTable( "P1/G2/L2/V2/ext4" ) );
[ [ 1, 1 ], [ 2, 2 ], [ 3, 2 ], [ 4, 2 ], [ 5, 1 ], [ 6, 5 ],
[ 10, 4 ], [ 12, 4 ], [ 15, 20 ], [ 20, 2 ], [ 30, 29 ], [ 60, 8 ] ]
gap> List( degrees, x -> x[1] ) = DivisorsInt( 60 );
true
## doc2/maintain.xml (1949-1961)
gap> BrokenSymmetries:= function( ordtbl, modtbl )
> local taut, maut, triv, fus, orb;
> taut:= AutomorphismsOfTable( ordtbl );
> maut:= AutomorphismsOfTable( modtbl );
> triv:= TrivialSubgroup( taut );
> fus:= GetFusionMap( modtbl, ordtbl );
> orb:= MakeImmutable( Set( OrbitFusions( maut, fus, triv ) ) );
> return ForAny( GeneratorsOfGroup( taut ),
> x -> ForAny( orb,
> fus -> not OnTuples( fus, x ) in orb ) );
> end;;
## doc2/maintain.xml (1994-2053)
gap> t:= CharacterTable( "2.A6.2_1" );;
gap> m:= t mod 2;;
gap> GetFusionMap( m, t );
[ 1, 4, 6, 9 ]
gap> AutomorphismsOfTable( t );
Group([ (16,17), (14,15), (14,15)(16,17) ])
gap> AutomorphismsOfTable( m );
Group([ (2,3) ])
gap> Display( m );
2.A6.2_1mod2
2 5 2 2 1
3 2 2 2 .
5 1 . . 1
1a 3a 3b 5a
2P 1a 3a 3b 5a
3P 1a 1a 1a 5a
5P 1a 3a 3b 1a
X.1 1 1 1 1
X.2 4 1 -2 -1
X.3 4 -2 1 -1
X.4 16 -2 -2 1
gap> Display( t );
2.A6.2_1
2 5 5 4 2 2 2 2 3 1 1 4 4 3 2 2 2 2
3 2 2 . 2 2 2 2 . . . 1 1 . 1 1 1 1
5 1 1 . . . . . . 1 1 . . . . . . .
1a 2a 4a 3a 6a 3b 6b 8a 5a 10a 2b 4b 8b 6c 6d 12a 12b
2P 1a 1a 2a 3a 3a 3b 3b 4a 5a 5a 1a 2a 4a 3a 3a 6b 6b
3P 1a 2a 4a 1a 2a 1a 2a 8a 5a 10a 2b 4b 8b 2b 2b 4b 4b
5P 1a 2a 4a 3a 6a 3b 6b 8a 1a 2a 2b 4b 8b 6d 6c 12b 12a
X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
X.2 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1
X.3 5 5 1 2 2 -1 -1 -1 . . 3 -1 1 . . -1 -1
X.4 5 5 1 2 2 -1 -1 -1 . . -3 1 -1 . . 1 1
X.5 5 5 1 -1 -1 2 2 -1 . . -1 3 1 -1 -1 . .
X.6 5 5 1 -1 -1 2 2 -1 . . 1 -3 -1 1 1 . .
X.7 16 16 . -2 -2 -2 -2 . 1 1 . . . . . . .
X.8 9 9 1 . . . . 1 -1 -1 3 3 -1 . . . .
X.9 9 9 1 . . . . 1 -1 -1 -3 -3 1 . . . .
X.10 10 10 -2 1 1 1 1 . . . 2 -2 . -1 -1 1 1
X.11 10 10 -2 1 1 1 1 . . . -2 2 . 1 1 -1 -1
X.12 4 -4 . -2 2 1 -1 . -1 1 . . . . . B -B
X.13 4 -4 . -2 2 1 -1 . -1 1 . . . . . -B B
X.14 4 -4 . 1 -1 -2 2 . -1 1 . . . A -A . .
X.15 4 -4 . 1 -1 -2 2 . -1 1 . . . -A A . .
X.16 16 -16 . -2 2 -2 2 . 1 -1 . . . . . . .
X.17 20 -20 . 2 -2 2 -2 . . . . . . . . . .
A = E(3)-E(3)^2
= Sqrt(-3) = i3
B = -E(12)^7+E(12)^11
= Sqrt(3) = r3
## doc2/maintain.xml (2092-2144)
gap> PrimesOfGeneralityProblems:= function( ordtbl )
> local consider, p, modtbl, taut, triv, admiss, fusion, maut,
> allfusions, orbits, orbit, reps;
> # Find the primes for which symmetries are broken.
> consider:= [];
> for p in Filtered( PrimeDivisors( Size( ordtbl ) ), IsPrimeInt ) do
> modtbl:= ordtbl mod p;
> if modtbl <> fail and BrokenSymmetries( ordtbl, modtbl ) then
> Add( consider, p );
> fi;
> od;
> # Compute the choices and detect generality problems.
> taut:= AutomorphismsOfTable( ordtbl );
> triv:= TrivialSubgroup( taut );
> admiss:= taut;
> for p in consider do
> modtbl:= ordtbl mod p;
> fusion:= GetFusionMap( modtbl, ordtbl );
> maut:= AutomorphismsOfTable( modtbl );
> # - We need not apply the action of 'maut' here,
> # since 'maut' will later be used to get representatives.
> # - We need not apply all elements in 'taut' but only
> # representatives of left cosets of 'admiss' in 'taut',
> # since 'admiss' will later be used to get representatives.
> # allfusions:= OrbitFusions( maut, fusion, taut );
> allfusions:= Set( RightTransversal( taut, admiss ),
> x -> OnTuples( fusion, x^-1 ) );
> # For computing representatives, 'RepresentativesFusions' is not
> # suitable because 'allfusions' is in generally not closed
> # under the actions.
> # reps:= RepresentativesFusions( maut, allfusions, admiss );
> orbits:= [];
> while not IsEmpty( allfusions ) do
> orbit:= OrbitFusions( maut, allfusions[1], admiss );
> Add( orbits, orbit );
> SubtractSet( allfusions, orbit );
> od;
> reps:= List( orbits, x -> x[1] );
> if Length( reps ) = 1 then
> # Reduce the symmetries that are still available.
> admiss:= Stabilizer( admiss,
> Set( OrbitFusions( maut, fusion, triv ) ),
> OnSetsTuples );
> else
> # We have found a generality problem.
> return consider;
> fi;
> od;
> # There is no generality problem for this table.
> return [];
> end;;
## doc2/maintain.xml (2161-2205)
gap> t:= CharacterTable( "2.A5.2" );;
gap> m:= t mod 5;;
gap> Display( m );
2.A5.2mod5
2 4 4 3 2 2 2 3 3 2 2
3 1 1 . 1 1 1 . . 1 1
5 1 1 . . . . . . . .
1a 2a 4a 3a 6a 2b 8a 8b 6b 6c
2P 1a 1a 2a 3a 3a 1a 4a 4a 3a 3a
3P 1a 2a 4a 1a 2a 2b 8a 8b 2b 2b
5P 1a 2a 4a 3a 6a 2b 8b 8a 6c 6b
X.1 1 1 1 1 1 1 1 1 1 1
X.2 1 1 1 1 1 -1 -1 -1 -1 -1
X.3 3 3 -1 . . 1 -1 -1 -2 -2
X.4 3 3 -1 . . -1 1 1 2 2
X.5 5 5 1 -1 -1 1 -1 -1 1 1
X.6 5 5 1 -1 -1 -1 1 1 -1 -1
X.7 2 -2 . -1 1 . A -A B -B
X.8 2 -2 . -1 1 . -A A -B B
X.9 4 -4 . 1 -1 . . . B -B
X.10 4 -4 . 1 -1 . . . -B B
A = E(8)+E(8)^3
= Sqrt(-2) = i2
B = E(3)-E(3)^2
= Sqrt(-3) = i3
gap> AutomorphismsOfTable( t );
Group([ (11,12), (9,10) ])
gap> AutomorphismsOfTable( m );
Group([ (7,8)(9,10) ])
gap> GetFusionMap( m, t );
[ 1, 2, 3, 4, 5, 8, 9, 10, 11, 12 ]
gap> BrokenSymmetries( t, m );
true
gap> BrokenSymmetries( t, t mod 2 );
false
gap> BrokenSymmetries( t, t mod 3 );
false
gap> PrimesOfGeneralityProblems( t );
[ ]
## doc2/maintain.xml (2227-2287)
gap> t:= CharacterTable( "J1" );;
gap> m:= t mod 11;;
gap> Display( m, rec( chars:= Filtered( Irr( m ), x -> x[1] = 7 ) ) );
J1mod11
2 3 3 1 1 1 1 . 1 1 . . . . .
3 1 1 1 1 1 1 . . . 1 1 . . .
5 1 1 1 1 1 . . 1 1 1 1 . . .
7 1 . . . . . 1 . . . . . . .
11 1 . . . . . . . . . . . . .
19 1 . . . . . . . . . . 1 1 1
1a 2a 3a 5a 5b 6a 7a 10a 10b 15a 15b 19a 19b 19c
2P 1a 1a 3a 5b 5a 3a 7a 5b 5a 15b 15a 19b 19c 19a
3P 1a 2a 1a 5b 5a 2a 7a 10b 10a 5b 5a 19b 19c 19a
5P 1a 2a 3a 1a 1a 6a 7a 2a 2a 3a 3a 19b 19c 19a
7P 1a 2a 3a 5b 5a 6a 1a 10b 10a 15b 15a 19a 19b 19c
11P 1a 2a 3a 5a 5b 6a 7a 10a 10b 15a 15b 19a 19b 19c
19P 1a 2a 3a 5a 5b 6a 7a 10a 10b 15a 15b 1a 1a 1a
Y.1 7 -1 1 A *A -1 . B *B C *C D E F
A = E(5)+E(5)^4
= (-1+Sqrt(5))/2 = b5
B = -E(5)-2*E(5)^2-2*E(5)^3-E(5)^4
= (3+Sqrt(5))/2 = 2+b5
C = -2*E(5)-2*E(5)^4
= 1-Sqrt(5) = 1-r5
D = -E(19)-E(19)^2-E(19)^3-E(19)^5-E(19)^7-E(19)^8-E(19)^11-E(19)^12-E\
(19)^14-E(19)^16-E(19)^17-E(19)^18
E = -E(19)^2-E(19)^3-E(19)^4-E(19)^5-E(19)^6-E(19)^9-E(19)^10-E(19)^13\
-E(19)^14-E(19)^15-E(19)^16-E(19)^17
F = -E(19)-E(19)^4-E(19)^6-E(19)^7-E(19)^8-E(19)^9-E(19)^10-E(19)^11-E\
(19)^12-E(19)^13-E(19)^15-E(19)^18
gap> m:= t mod 19;;
gap> Display( m, rec( chars:= Filtered( Irr( m ), x -> x[1] = 22 ) ) );
J1mod19
2 3 3 1 1 1 1 . 1 1 . . .
3 1 1 1 1 1 1 . . . . 1 1
5 1 1 1 1 1 . . 1 1 . 1 1
7 1 . . . . . 1 . . . . .
11 1 . . . . . . . . 1 . .
19 1 . . . . . . . . . . .
1a 2a 3a 5a 5b 6a 7a 10a 10b 11a 15a 15b
2P 1a 1a 3a 5b 5a 3a 7a 5b 5a 11a 15b 15a
3P 1a 2a 1a 5b 5a 2a 7a 10b 10a 11a 5b 5a
5P 1a 2a 3a 1a 1a 6a 7a 2a 2a 11a 3a 3a
7P 1a 2a 3a 5b 5a 6a 1a 10b 10a 11a 15b 15a
11P 1a 2a 3a 5a 5b 6a 7a 10a 10b 1a 15a 15b
19P 1a 2a 3a 5a 5b 6a 7a 10a 10b 11a 15a 15b
Y.1 22 -2 1 A *A 1 1 -A -*A . B *B
A = E(5)+E(5)^4
= (-1+Sqrt(5))/2 = b5
B = -2*E(5)-2*E(5)^4
= 1-Sqrt(5) = 1-r5
## doc2/maintain.xml (2300-2303)
gap> PrimesOfGeneralityProblems( t );
[ 7, 11, 19 ]
## doc2/maintain.xml (2312-2465)
gap> list:= [];;
gap> isGeneralityProblem:= function( ordtbl )
> local res;
> res:= PrimesOfGeneralityProblems( ordtbl );
> if res = [] then
> return false;
> fi;
> Add( list, [ Identifier( ordtbl ), res ] );
> return true;
> end;;
gap> AllCharacterTableNames( IsDuplicateTable, false,
> isGeneralityProblem, true );;
gap> PrintArray( SortedList( list ) );
[ [ (2.A4x2.G2(4)).2, [ 2, 5, 7, 13 ] ],
[ (2^2x3).L3(4).2_1, [ 5, 7 ] ],
[ (2x12).L3(4), [ 2, 3, 7 ] ],
[ (4^2x3).L3(4), [ 2, 3, 7 ] ],
[ (7:3xHe):2, [ 5, 7, 17 ] ],
[ (A5xA12):2, [ 2, 3 ] ],
[ (D10xHN).2, [ 2, 3, 5, 7, 11, 19 ] ],
[ (S3x2.Fi22).2, [ 3, 11, 13 ] ],
[ 12.M22, [ 2, 5, 7, 11 ] ],
[ 12.M22.2, [ 2, 5, 7, 11 ] ],
[ 12_1.L3(4).2_1, [ 5, 7 ] ],
[ 12_2.L3(4), [ 2, 3, 7 ] ],
[ 12_2.L3(4).2_1, [ 3, 5, 7 ] ],
[ 12_2.L3(4).2_2, [ 2, 3, 7 ] ],
[ 12_2.L3(4).2_3, [ 2, 3, 7 ] ],
[ 2.(A4xG2(4)).2, [ 2, 5, 7, 13 ] ],
[ 2.2E6(2), [ 13, 19 ] ],
[ 2.2E6(2).2, [ 13, 19 ] ],
[ 2.A10, [ 5, 7 ] ],
[ 2.A11, [ 3, 5, 7 ] ],
[ 2.A11.2, [ 5, 7, 11 ] ],
[ 2.A12, [ 2, 3, 5, 7 ] ],
[ 2.A12.2, [ 5, 7, 11 ] ],
[ 2.A13, [ 2, 3, 5, 7, 11 ] ],
[ 2.A13.2, [ 5, 7, 13 ] ],
[ 2.Alt(14), [ 2, 3, 5, 7 ] ],
[ 2.Alt(15), [ 2, 5, 7 ] ],
[ 2.Alt(16), [ 2, 3, 5, 7 ] ],
[ 2.Alt(17), [ 2, 3, 5, 7 ] ],
[ 2.Alt(18), [ 2, 3, 5, 7 ] ],
[ 2.B, [ 17, 23 ] ],
[ 2.F4(2), [ 2, 7, 13, 17 ] ],
[ 2.Fi22.2, [ 11, 13 ] ],
[ 2.G2(4), [ 2, 7 ] ],
[ 2.G2(4).2, [ 5, 7, 13 ] ],
[ 2.HS, [ 3, 5, 7, 11 ] ],
[ 2.HS.2, [ 3, 11 ] ],
[ 2.L3(4).2_1, [ 5, 7 ] ],
[ 2.Ru, [ 5, 7, 13, 29 ] ],
[ 2.Suz, [ 2, 5, 11 ] ],
[ 2.Suz.2, [ 3, 7, 13 ] ],
[ 2.Sym(15), [ 3, 5, 7 ] ],
[ 2.Sym(16), [ 3, 5, 7 ] ],
[ 2.Sym(17), [ 3, 5, 7 ] ],
[ 2.Sym(18), [ 5, 7 ] ],
[ 2.Sz(8), [ 2, 5, 13 ] ],
[ 2^2.2E6(2), [ 13, 19 ] ],
[ 2^2.2E6(2).2, [ 13, 19 ] ],
[ 2^2.Fi22.2, [ 3, 11, 13 ] ],
[ 2^2.L3(4).2^2, [ 5, 7 ] ],
[ 2^2.L3(4).2_1, [ 5, 7 ] ],
[ 2^2.Sz(8), [ 2, 5, 13 ] ],
[ 2x2.F4(2), [ 2, 7, 13, 17 ] ],
[ 2x3.Fi22, [ 2, 3, 5 ] ],
[ 2x6.Fi22, [ 2, 3, 5 ] ],
[ 2x6.M22, [ 2, 5, 11 ] ],
[ 2xFi22.2, [ 11, 13 ] ],
[ 2xFi23, [ 3, 17, 23 ] ],
[ 3.Fi22, [ 2, 3, 5 ] ],
[ 3.Fi22.2, [ 2, 5, 11, 13 ] ],
[ 3.J3, [ 2, 17, 19 ] ],
[ 3.J3.2, [ 2, 5, 17, 19 ] ],
[ 3.L3(4).2_3, [ 2, 3, 7 ] ],
[ 3.L3(4).3.2_3, [ 2, 3, 7 ] ],
[ 3.L3(7).2, [ 3, 7, 19 ] ],
[ 3.L3(7).S3, [ 3, 7, 19 ] ],
[ 3.McL, [ 2, 5, 11 ] ],
[ 3.McL.2, [ 2, 3, 5, 11 ] ],
[ 3.ON, [ 3, 7, 11, 19, 31 ] ],
[ 3.ON.2, [ 3, 5, 7, 11, 19, 31 ] ],
[ 3.Suz.2, [ 2, 3, 13 ] ],
[ 3x2.F4(2), [ 2, 7, 13, 17 ] ],
[ 3x2.Fi22.2, [ 11, 13 ] ],
[ 3x2.G2(4), [ 2, 7 ] ],
[ 3xFi23, [ 3, 17, 23 ] ],
[ 3xJ1, [ 7, 11, 19 ] ],
[ 3xL3(7).2, [ 3, 7, 19 ] ],
[ 4.HS.2, [ 5, 7, 11 ] ],
[ 4.M22, [ 5, 7 ] ],
[ 4_1.L3(4).2_1, [ 5, 7 ] ],
[ 4_2.L3(4).2_1, [ 3, 5, 7 ] ],
[ 6.Fi22, [ 2, 3, 5 ] ],
[ 6.Fi22.2, [ 2, 5, 11, 13 ] ],
[ 6.L3(4).2_1, [ 5, 7 ] ],
[ 6.M22, [ 2, 5, 11 ] ],
[ 6.O7(3), [ 3, 5, 13 ] ],
[ 6.O7(3).2, [ 3, 5, 13 ] ],
[ 6.Suz, [ 2, 5, 11 ] ],
[ 6.Suz.2, [ 2, 3, 5, 7, 13 ] ],
[ 6x2.F4(2), [ 2, 7, 13, 17 ] ],
[ A12, [ 2, 3 ] ],
[ A14, [ 2, 5, 7 ] ],
[ A17, [ 2, 7 ] ],
[ A18, [ 2, 3, 5, 7 ] ],
[ B, [ 13, 17, 23, 31 ] ],
[ F3+, [ 17, 23, 29 ] ],
[ F3+.2, [ 17, 23, 29 ] ],
[ Fi22.2, [ 11, 13 ] ],
[ Fi23, [ 3, 17, 23 ] ],
[ HN, [ 2, 3, 11, 19 ] ],
[ HN.2, [ 5, 7, 11, 19 ] ],
[ He, [ 5, 17 ] ],
[ He.2, [ 5, 7, 17 ] ],
[ Isoclinic(12.M22.2), [ 2, 5, 7, 11 ] ],
[ Isoclinic(12_1.L3(4).2_1), [ 5, 7 ] ],
[ Isoclinic(12_2.L3(4).2_1), [ 3, 5, 7 ] ],
[ Isoclinic(12_2.L3(4).2_3), [ 2, 3, 7 ] ],
[ Isoclinic(2.A11.2), [ 5, 7, 11 ] ],
[ Isoclinic(2.A12.2), [ 5, 7, 11 ] ],
[ Isoclinic(2.A13.2), [ 5, 7, 13 ] ],
[ Isoclinic(2.Fi22.2), [ 11, 13 ] ],
[ Isoclinic(2.G2(4).2), [ 5, 7, 13 ] ],
[ Isoclinic(2.HS.2), [ 3, 11 ] ],
[ Isoclinic(2.HSx2), [ 3, 5, 7, 11 ] ],
[ Isoclinic(2.L3(4).2_1), [ 5, 7 ] ],
[ Isoclinic(2.Suz.2), [ 3, 7, 13 ] ],
[ Isoclinic(4_1.L3(4).2_1), [ 5, 7 ] ],
[ Isoclinic(4_2.L3(4).2_1), [ 3, 5, 7 ] ],
[ Isoclinic(6.Fi22.2), [ 2, 5, 11, 13 ] ],
[ Isoclinic(6.L3(4).2_1), [ 5, 7 ] ],
[ Isoclinic(6.O7(3).2), [ 3, 5, 13 ] ],
[ Isoclinic(6.Suz.2), [ 2, 3, 5, 7, 13 ] ],
[ J1, [ 7, 11, 19 ] ],
[ J1x2, [ 7, 11, 19 ] ],
[ J3, [ 2, 17, 19 ] ],
[ J3.2, [ 2, 5, 17, 19 ] ],
[ L3(4).2_3, [ 3, 7 ] ],
[ L3(4).3.2_3, [ 2, 3, 7 ] ],
[ L3(7).2, [ 3, 7, 19 ] ],
[ L3(7).S3, [ 3, 7, 19 ] ],
[ L3(9).2_1, [ 3, 7, 13 ] ],
[ L5(2).2, [ 2, 7, 31 ] ],
[ Ly, [ 7, 37, 67 ] ],
[ M23, [ 2, 3, 23 ] ],
[ ON, [ 3, 7, 11, 19, 31 ] ],
[ ON.2, [ 3, 5, 7, 11, 19, 31 ] ],
[ Ru, [ 5, 7, 13, 29 ] ],
[ S3xFi22.2, [ 11, 13 ] ],
[ Suz.2, [ 3, 13 ] ] ]
## doc2/maintain.xml (2513-2530)
gap> t:= CharacterTable( "J3" );;
gap> m:= t mod 19;;
gap> cand:= Filtered( Irr( m ), x -> x[1] = 110 );;
gap> Length( cand );
1
gap> slp:= AtlasProgram( "J3", "classes" );;
gap> 17a:= Position( slp.outputs, "17A" );
18
gap> info:= OneAtlasGeneratingSetInfo( "J3", Characteristic, 19,
> Dimension, 110 );;
gap> gens:= AtlasGenerators( info );;
gap> reps:= ResultOfStraightLineProgram( slp.program,
> gens.generators );;
gap> Quadratic( BrauerCharacterValue( reps[ 17a ] ) );
rec( ATLAS := "-1-b17", a := -1, b := -1, d := 2,
display := "(-1-Sqrt(17))/2", root := 17 )
## doc2/maintain.xml (2641-2665)
gap> table:= [];;
gap> for pair in [ [ 2, [ 78, 80, 244, 966 ] ],
> [ 19, [ 110, 214, 706 ] ] ] do
> p:= pair[1];
> for d in pair[2] do
> info:= OneAtlasGeneratingSetInfo( "J3", Characteristic, p,
> Dimension, d );
> gens:= AtlasGenerators( info );
> reps:= ResultOfStraightLineProgram( slp.program,
> gens.generators );
> val:= BrauerCharacterValue( reps[ 17a ] );
> Add( table, [ p, d, Quadratic( val ).ATLAS,
> Quadratic( StarCyc( val ) ).ATLAS ] );
> od;
> od;
gap> PrintArray( table );
[ [ 2, 78, 1-b17, 2+b17 ],
[ 2, 80, 3-b17, 4+b17 ],
[ 2, 244, -2+b17, -3-b17 ],
[ 2, 966, -3+r17, -3-r17 ],
[ 19, 110, -1-b17, b17 ],
[ 19, 214, 2+b17, 1-b17 ],
[ 19, 706, 1+b17, -b17 ] ]
## doc2/maintain.xml (2770-2777)
gap> t:= CharacterTable( "HN" );;
gap> pos20:= Positions( OrdersClassRepresentatives( t ), 20 );
[ 39, 40, 41, 42, 43 ]
gap> diff:= Filtered( Irr( t ), x -> x[39] <> x[40] );;
gap> List( diff, x -> Position( Irr( t ), x ) );
[ 51, 52 ]
## doc2/maintain.xml (2786-2790)
gap> List( diff, x -> List( x{ [ 1, 39, 40 ] },
> CTblLib.StringOfAtlasIrrationality ) );
[ [ "5103000", "2r5+1", "-2r5+1" ], [ "5103000", "-2r5+1", "2r5+1" ] ]
## doc2/maintain.xml (2814-2826)
gap> t11:= t mod 11;;
gap> rest11:= RestrictedClassFunctions( diff, t11 );;
gap> dec11:= Decomposition( Irr( t11 ), rest11, "nonnegative" );;
gap> List( dec11, Set );
[ [ 0, 1 ], [ 0, 1 ] ]
gap> List( dec11, x -> Positions( x, 1 ) );
[ [ 40, 48 ], [ 39, 49 ] ]
gap> List( Irr( t11 ){ [ 40, 48 ] }, x -> x[1] );
[ 1575176, 3527824 ]
gap> List( Irr( t11 ){ [ 39, 49 ] }, x -> x[1] );
[ 1361919, 3741081 ]
## doc2/maintain.xml (2842-2854)
gap> t19:= t mod 19;;
gap> rest19:= RestrictedClassFunctions( diff, t19 );;
gap> dec19:= Decomposition( Irr( t19 ), rest19, "nonnegative" );;
gap> List( dec19, Set );
[ [ 0, 1 ], [ 0, 1 ] ]
gap> List( dec19, x -> Positions( x, 1 ) );
[ [ 42, 45 ], [ 33, 48 ] ]
gap> List( Irr( t19 ){ [ 42, 45 ] }, x -> x[1] );
[ 2125925, 2977075 ]
gap> List( Irr( t19 ){ [ 33, 48 ] }, x -> x[1] );
[ 1197330, 3905670 ]
## doc2/maintain.xml (2867-2872)
gap> Indicator( t11, 2 ){ [ 39, 40, 48, 49 ] };
[ 1, 1, 1, 1 ]
gap> Indicator( t19, 2 ){ [ 33, 42, 45, 48 ] };
[ 1, 1, 1, 1 ]
## doc2/maintain.xml (3061-3068)
gap> t:= CharacterTable( PSL( 2, 11 ) );;
gap> modt:= t mod 5;;
gap> modt <> fail;
true
gap> InfoText( modt );
"computed using that all Brauer characters lift to char. zero"
## doc2/maintain.xml (3077-3088)
gap> lib:= CharacterTable( "M11" );;
gap> fromgroup:= CharacterTable( MathieuGroup( 11 ) );;
gap> DecompositionMatrix( lib mod 5 );
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 1, 1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ]
gap> fromgroup mod 5 <> fail;
true
## doc2/maintain.xml (3099-3107)
gap> DecompositionMatrix( lib mod 2 );
[ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0 ], [ 1, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ], [ 1, 0, 0, 0, 1 ],
[ 1, 1, 0, 0, 1 ] ]
gap> fromgroup mod 2;
fail
## doc2/maintain.xml (3148-3154)
gap> s:= CharacterTable( "2.U4(2)" );;
gap> m:= CharacterTable( "M" );;
gap> sfusm:= PossibleClassFusions( s, m, rec( decompose:= false ) );;
gap> Length( sfusm );
2332
## doc2/maintain.xml (3169-3177)
gap> Set( List( sfusm, x -> x[2] ) );
[ 3 ]
gap> t:= CharacterTable( "MN2B" );
CharacterTable( "2^1+24.Co1" )
gap> sfust:= PossibleClassFusions( s, t, rec( decompose:= false ) );;
gap> Length( sfust );
0
## doc2/maintain.xml (3203-3216)
gap> simp:= CharacterTable( "L3(4)" );;
gap> extnames:= AllCharacterTableNames( Identifier,
> x -> EndsWith(x, "L3(4)" ) );;
gap> ext:= List( extnames, CharacterTable );;
gap> ext:= Filtered( ext, x -> Length( ClassPositionsOfCentre( x ) ) =
> Size( x ) / Size( simp ) );;
gap> SortBy( ext, Size );
gap> names:= List( ext, Identifier );
[ "L3(4)", "2.L3(4)", "3.L3(4)", "2^2.L3(4)", "4_1.L3(4)",
"4_2.L3(4)", "6.L3(4)", "(2x4).L3(4)", "(2^2x3).L3(4)",
"12_1.L3(4)", "12_2.L3(4)", "4^2.L3(4)", "(2x12).L3(4)",
"(4^2x3).L3(4)" ]
## doc2/maintain.xml (3253-3263)
gap> Length( PossibleClassFusions( CharacterTable( "L3(4)" ),
> CharacterTable( "2.U4(3)" ) ) );
0
gap> Length( PossibleClassFusions( CharacterTable( "3.L3(4)" ),
> CharacterTable( "2.G2(4)" ) ) );
0
gap> Length( PossibleClassFusions( CharacterTable( "G2(4)" ),
> CharacterTable( "2.Suz" ) ) );
0
## doc2/maintain.xml (3278-3283)
gap> t:= CharacterTable( "MN3B" );
CharacterTable( "3^(1+12).2.Suz.2" )
gap> Length( PossibleClassFusions( CharacterTable( "3.L3(4)" ), t ) );
0
## doc2/maintain.xml (3298-3303)
gap> mx:= List( Maxes( CharacterTable( "Fi24'" ) ), CharacterTable );;
gap> s:= CharacterTable( "L3(4)" );;
gap> Filtered( mx, x -> Length( PossibleClassFusions( s, x ) ) > 0 );
[ CharacterTable( "Fi23" ) ]
## doc2/maintain.xml (3318-3353)
gap> done:= [ "L3(4)", "2.L3(4)", "3.L3(4)", "2^2.L3(4)", "6.L3(4)" ];;
gap> names:= Filtered( names, x -> not x in done );
[ "4_1.L3(4)", "4_2.L3(4)", "(2x4).L3(4)", "(2^2x3).L3(4)",
"12_1.L3(4)", "12_2.L3(4)", "4^2.L3(4)", "(2x12).L3(4)",
"(4^2x3).L3(4)" ]
gap> invcent:= List( [ "MN2A", "MN2B" ], CharacterTable );
[ CharacterTable( "2.B" ), CharacterTable( "2^1+24.Co1" ) ]
gap> ForAll( invcent, x -> ClassPositionsOfCentre( x ) = [ 1, 2 ] );
true
gap> cand:= [];;
gap> ords:= "dummy";; # Avoid a message about an unbound variable ...
gap> for name in names do
> s:= CharacterTable( name );
> ords:= OrdersClassRepresentatives( s );
> invpos:= Filtered( ClassPositionsOfCentre( s ), i -> ords[i] = 2 );
> for i in invpos do
> for t in invcent do
> init:= InitFusion( s, t );
> if init = fail then
> continue;
> fi;
> init[i]:= 2;
> fus:= PossibleClassFusions( s, t, rec( fusionmap:= init,
> decompose:= false ) );
> if fus <> [] then
> Add( cand, [ s, t, i, fus ] );
> fi;
> od;
> od;
> od;
gap> List( cand, x -> x{ [ 1 .. 3 ] } );
[ [ CharacterTable( "4_1.L3(4)" ), CharacterTable( "2^1+24.Co1" ), 3 ]
, [ CharacterTable( "(2x4).L3(4)" ), CharacterTable( "2.B" ), 2 ],
[ CharacterTable( "(2x4).L3(4)" ), CharacterTable( "2.B" ), 3 ] ]
## doc2/maintain.xml (3391-3411)
gap> s:= cand[1][1];
CharacterTable( "4_1.L3(4)" )
gap> t:= cand[1][2];
CharacterTable( "2^1+24.Co1" )
gap> fus:= cand[1][4];
[ [ 1, 5, 2, 5, 9, 8, 23, 27, 24, 27, 49, 49, 50, 50, 70, 74, 71, 74,
70, 74, 71, 74, 114, 119, 115, 119, 114, 119, 115, 119 ] ]
gap> ClassPositionsOfCentre( s );
[ 1, 2, 3, 4 ]
gap> 5 in ClassPositionsOfPCore( t, 2 );
true
gap> siz:= SizesCentralizers( t )[5] / 2^24;
495766656000
gap> mx:= Filtered( List( Maxes( CharacterTable( "Co1" ) ),
> CharacterTable ),
> x -> Size( x ) mod siz = 0 );
[ CharacterTable( "Co3" ) ]
gap> Size( mx[1] ) = siz;
true
## doc2/maintain.xml (3437-3449)
gap> tblH:= CharacterTable( "(3^2:2xO8+(3)).S4" );
CharacterTable( "(3^2:2xO8+(3)).S4" )
gap> N:= ClassPositionsOfSolvableResiduum( tblH );;
gap> tblF:= tblH / N;;
gap> Size( tblF );
432
gap> known:= NamesOfEquivalentLibraryCharacterTables( tblF );
[ "3^2.2.S4", "M12M7" ]
gap> Filtered( GroupInfoForCharacterTable( known[1] ),
> x -> x[1] = "SmallGroup" );
[ [ "SmallGroup", [ 432, 734 ] ] ]
## doc2/maintain.xml (3467-3472)
gap> G:= SmallGroup( 432, 734 );;
gap> P:= PCore( G, 3 );;
gap> Length( ComplementClassesRepresentatives( G, P ) );
1
## doc2/maintain.xml (3488-3507)
gap> tblV:= tblH / ClassPositionsOfPCore( tblH, 3 );;
gap> ord:= 2 * Size( tblH ) / Size( tblF );
9904359628800
gap> classes:= SizesConjugacyClasses( tblV );;
gap> 2N:= Filtered( ClassPositionsOfNormalSubgroups( tblV ),
> l -> Sum( classes{ l } ) = ord );;
gap> Length( 2N );
1
gap> Set( OrdersClassRepresentatives( tblV ){ 2N[1] } );
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20, 26, 30 ]
gap> Set( OrdersClassRepresentatives( CharacterTable( "O8+(3)" ) ) );
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20 ]
gap> Set( OrdersClassRepresentatives( CharacterTable( "O8+(3).2_1" ) ) );
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20, 24, 26, 28,
30, 36, 40 ]
gap> Set( OrdersClassRepresentatives( CharacterTable( "O8+(3).2_2" ) ) );
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20, 24, 26, 28,
30, 36 ]
## doc2/maintain.xml (3517-3526)
gap> tblM:= CharacterTable( "M" );;
gap> VfusM:= PossibleClassFusions( tblV, tblM );;
gap> Length( VfusM );
4
gap> ZV:= ClassPositionsOfCentre( tblV );
[ 1, 2 ]
gap> Set( List( VfusM, l -> l{ ZV } ) );
[ [ 1, 2 ] ]
## doc2/maintain.xml (3537-3542)
gap> tblB:= CharacterTable( "B" );;
gap> mxB:= List( Maxes( tblB ), CharacterTable );;
gap> cand:= Filtered( mxB, s -> Size( s ) mod ( Size( tblV ) / 2 ) = 0 );
[ CharacterTable( "Fi23" ), CharacterTable( "O8+(3).S4" ) ]
## doc2/maintain.xml (3551-3554)
gap> Length( PossibleClassFusions( tblV / ZV, CharacterTable( "Fi23" ) ) );
0
## doc2/maintain.xml (3573-3579)
gap> lib:= CharacterTable( "(2xO8+(3)).S4" );;
gap> TransformingPermutationsCharacterTables( tblV, lib ) <> fail;
true
gap> Irr( lib ) = Irr( tblV );
true
## doc2/maintain.xml (3592-3600)
gap> tblU:= CharacterTable( "O8+(3).S4" );;
gap> tbl2B:= CharacterTable( "2.B" );;
gap> CompositionMaps( GetFusionMap( tblU, tblB ),
> GetFusionMap( lib, tblU ) ) =
> CompositionMaps( GetFusionMap( tbl2B, tblB ),
> GetFusionMap( lib, tbl2B ) );
true
## doc2/maintain.xml (3609-3616)
gap> tblH:= CharacterTable( "(3^2:2xO8+(3)).S4" );;
gap> CompositionMaps( GetFusionMap( tblH, tblM ),
> GetFusionMap( lib, tblH ) ) =
> CompositionMaps( GetFusionMap( tbl2B, tblM ),
> GetFusionMap( lib, tbl2B ) );
true
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> data.replayInterval:= oldinterval;
> fi;
##
gap> STOP_TEST( "maintain.tst" );
gap> SizeScreen( save );;
#############################################################################
##
#E
[ Dauer der Verarbeitung: 0.17 Sekunden
(vorverarbeitet)
]
|
2026-04-02
|
