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# This file was created automatically, do not edit!
#############################################################################
##
#W ctocenex.tst GAP 4 package CTblLib Thomas Breuer
##
#Y Copyright (C) 2020, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
##
## 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( "ctocenex.tst" );'.
##
gap> LoadPackage( "CTblLib", false );
true
gap> save:= SizeScreen();;
gap> SizeScreen( [ 72 ] );;
gap> START_TEST( "ctocenex.tst" );
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> oldinterval:= data.replayInterval;
> data.replayInterval:= 1;
> fi;
## ./ctocenex.xml (590-593)
gap> LoadPackage( "ctbllib", false );
true
## ./ctocenex.xml (613-634)
gap> list:= [
> # G m.G n.G mn.G
>
> [ "A6", "2.A6", "3.A6", "6.A6" ],
> [ "A7", "2.A7", "3.A7", "6.A7" ],
> [ "L3(4)", "2.L3(4)", "3.L3(4)", "6.L3(4)" ],
> [ "2.L3(4)", "4_1.L3(4)", "6.L3(4)", "12_1.L3(4)" ],
> [ "2.L3(4)", "4_2.L3(4)", "6.L3(4)", "12_2.L3(4)" ],
> [ "M22", "2.M22", "3.M22", "6.M22" ],
> [ "2.M22", "4.M22", "6.M22", "12.M22" ],
> [ "U4(3)", "2.U4(3)", "3_1.U4(3)", "6_1.U4(3)" ],
> [ "U4(3)", "2.U4(3)", "3_2.U4(3)", "6_2.U4(3)" ],
> [ "2.U4(3)", "4.U4(3)", "6_1.U4(3)", "12_1.U4(3)" ],
> [ "2.U4(3)", "4.U4(3)", "6_2.U4(3)", "12_2.U4(3)" ],
> [ "O7(3)", "2.O7(3)", "3.O7(3)", "6.O7(3)" ],
> [ "U6(2)", "2.U6(2)", "3.U6(2)", "6.U6(2)" ],
> [ "Suz", "2.Suz", "3.Suz", "6.Suz" ],
> [ "Fi22", "2.Fi22", "3.Fi22", "6.Fi22" ],
> [ "2E6(2)", "2.2E6(2)", "3.2E6(2)", "6.2E6(2)" ],
> ];;
## ./ctocenex.xml (651-707)
gap> SetInfoLevel( InfoCharacterTable, 1 );
gap> for entry in list do
> id := entry[4];
> tblG := CharacterTable( entry[1] );
> tblmG := CharacterTable( entry[2] );
> tblnG := CharacterTable( entry[3] );
> lib := CharacterTable( id );
> res:= CharacterTableOfCommonCentralExtension( tblG, tblmG, tblnG, id );
> if not res.IsComplete then
> Print( "#E not complete: ", id, "\n" );
> fi;
> if not IsSubset( Irr( lib ), res.irreducibles ) then
> Print( "#E inconsistent: ", id, "\n" );
> fi;
> od;
#I 6.A6: need 4 faithful irreducibles
#I 6.A6: 4 found by tensoring
#I 6.A7: need 5 faithful irreducibles
#I 6.A7: 5 found by tensoring
#I 6.L3(4): need 7 faithful irreducibles
#I 6.L3(4): 7 found by LLL
#I 12_1.L3(4): need 5 faithful irreducibles
#I 12_1.L3(4): 2 found by tensoring
#I 12_1.L3(4): 3 found by tensoring
#I 12_2.L3(4): need 6 faithful irreducibles
#I 12_2.L3(4): 6 found by LLL
#I 6.M22: need 10 faithful irreducibles
#I 6.M22: 1 found by tensoring
#I 6.M22: 9 found by LLL
#I 12.M22: need 7 faithful irreducibles
#I 12.M22: 7 found by LLL
#I 6_1.U4(3): need 15 faithful irreducibles
#I 6_1.U4(3): 1 found by tensoring
#I 6_1.U4(3): 14 found by LLL
#I 6_2.U4(3): need 12 faithful irreducibles
#I 6_2.U4(3): 12 found by LLL
#I 12_1.U4(3): need 12 faithful irreducibles
#I 12_1.U4(3): 4 found by tensoring
#I 12_1.U4(3): 8 found by tensoring
#I 12_2.U4(3): need 9 faithful irreducibles
#I 12_2.U4(3): 9 found by LLL
#I 6.O7(3): need 12 faithful irreducibles
#I 6.O7(3): 2 found by tensoring
#I 6.O7(3): 10 found by LLL
#I 6.U6(2): need 28 faithful irreducibles
#I 6.U6(2): 2 found by tensoring
#I 6.U6(2): 26 found by LLL
#I 6.Suz: need 29 faithful irreducibles
#I 6.Suz: 29 found by LLL
#I 6.Fi22: need 34 faithful irreducibles
#I 6.Fi22: 4 found by tensoring
#I 6.Fi22: 30 found by LLL
#I 6.2E6(2): need 60 faithful irreducibles
#I 6.2E6(2): 60 found by LLL
gap> SetInfoLevel( InfoCharacterTable, 0 );
## ./ctocenex.xml (757-763)
gap> list2:= [
> [ "2.L3(4)", "2^2.L3(4)", "6.L3(4)", "(2^2x3).L3(4)" ],
> [ "2^2.L3(4)", "(2x4).L3(4)", "(2^2x3).L3(4)", "(2x12).L3(4)" ],
> [ "(2x4).L3(4)", "4^2.L3(4)", "(2x12).L3(4)", "(4^2x3).L3(4)" ],
> ];;
## ./ctocenex.xml (794-841)
gap> Append( list2, [
> [ "3_1.U4(3)", "6_1.U4(3)", "3^2.U4(3)", "(3^2x2).U4(3)" ],
> [ "3_2.U4(3)", "6_2.U4(3)", "3^2.U4(3)", "(3^2x2).U4(3)" ],
> [ "6_1.U4(3)", "12_1.U4(3)", "(3^2x2).U4(3)", "(3^2x4).U4(3)" ],
> [ "6_2.U4(3)", "12_2.U4(3)", "(3^2x2).U4(3)", "(3^2x4).U4(3)" ],
> ] );
gap> SetInfoLevel( InfoCharacterTable, 1 );
gap> for entry in list2 do
> id := entry[4];
> tblG := CharacterTable( entry[1] );
> tblmG := CharacterTable( entry[2] );
> tblnG := CharacterTable( entry[3] );
> lib := CharacterTable( id );
> res:= CharacterTableOfCommonCentralExtension(
> tblG, tblmG, tblnG, id );
> if not res.IsComplete then
> Print( "#E not complete: ", id, "\n" );
> fi;
> if TransformingPermutationsCharacterTables( res.tblmnG, lib )
> = fail then
> Print( "#E inconsistent: ", id, "\n" );
> fi;
> od;
#I (2^2x3).L3(4): need 14 faithful irreducibles
#I (2^2x3).L3(4): 14 found by tensoring
#I (2x12).L3(4): need 11 faithful irreducibles
#I (2x12).L3(4): 7 found by tensoring
#I (2x12).L3(4): 4 found by LLL
#I (4^2x3).L3(4): need 22 faithful irreducibles
#I (4^2x3).L3(4): 14 found by tensoring
#I (4^2x3).L3(4): 8 found by LLL
#I (3^2x2).U4(3): need 39 faithful irreducibles
#I (3^2x2).U4(3): 27 found by tensoring
#I (3^2x2).U4(3): 12 found by LLL
#I (3^2x2).U4(3): need 42 faithful irreducibles
#I (3^2x2).U4(3): 2 found by tensoring
#I (3^2x2).U4(3): 40 found by LLL
#I (3^2x4).U4(3): need 30 faithful irreducibles
#I (3^2x4).U4(3): 6 found by tensoring
#I (3^2x4).U4(3): 8 found by tensoring
#I (3^2x4).U4(3): 16 found by LLL
#I (3^2x4).U4(3): need 33 faithful irreducibles
#I (3^2x4).U4(3): 9 found by tensoring
#I (3^2x4).U4(3): 18 found by tensoring
#I (3^2x4).U4(3): 6 found by further tensoring
gap> SetInfoLevel( InfoCharacterTable, 0 );
## ./ctocenex.xml (865-897)
gap> sublist:= list{ [ 6, 7, 14 ] };
[ [ "M22", "2.M22", "3.M22", "6.M22" ],
[ "2.M22", "4.M22", "6.M22", "12.M22" ],
[ "Suz", "2.Suz", "3.Suz", "6.Suz" ] ]
gap> for entry in sublist do
> tblG := CharacterTable( entry[1] );
> tblmG := CharacterTable( entry[2] );
> tblnG := CharacterTable( entry[3] );
> lib := CharacterTable( entry[4] );
>
> maxesG := List( Maxes( tblG ), CharacterTable );
> maxesmG := List( Maxes( tblmG ), CharacterTable );
> maxesnG := List( Maxes( tblnG ), CharacterTable );
> maxeslib := List( Maxes( lib ), CharacterTable );
>
> for i in [ 1 .. Length( maxesG ) ] do
> id:= Identifier( maxeslib[i] );
> res:= CharacterTableOfCommonCentralExtension( maxesG[i],
> maxesmG[i], maxesnG[i], id );
> if not res.IsComplete then
> Print( "#E not complete: ", id, "\n" );
> fi;
> if not IsSubset( Irr( maxeslib[i] ), res.irreducibles ) then
> trans:= TransformingPermutationsCharacterTables( maxeslib[i],
> res.tblmnG );
> if not IsRecord( trans ) then
> Print( "#E not transformable: ", id, "\n" );
> fi;
> fi;
> od;
> od;
## ./ctocenex.xml (959-963)
gap> tblmG := CharacterTable( "F3+N2B" );;
gap> tblG := tblmG / ClassPositionsOfCentre( tblmG );;
gap> tblnG := CharacterTable( "2^12.3^2.U4(3).2_2'" );;
## ./ctocenex.xml (973-982)
gap> f2:= tblnG / ClassPositionsOfCentre( tblnG );;
gap> trans:= TransformingPermutationsCharacterTables( f2, tblG );;
gap> tblnGfustblG:= OnTuples( GetFusionMap( tblnG, f2 ),
> trans.columns );;
gap> StoreFusion( tblnG, tblnGfustblG, tblG );
gap> IsSubset( Irr( tblnG ),
> List( Irr( tblG ), x -> x{ tblnGfustblG } ) );
true
## ./ctocenex.xml (991-1000)
gap> SetInfoLevel( InfoCharacterTable, 1 );
gap> id:= "3.2^(1+12).3U4(3).2";;
gap> res:= CharacterTableOfCommonCentralExtension(
> tblG, tblmG, tblnG, id );;
#I 3.2^(1+12).3U4(3).2: need 36 faithful irreducibles
#I 3.2^(1+12).3U4(3).2: 16 found by tensoring
#I 3.2^(1+12).3U4(3).2: 20 found by LLL
gap> SetInfoLevel( InfoCharacterTable, 0 );
## ./ctocenex.xml (1010-1015)
gap> lib:= CharacterTable( "3.F3+N2B" );;
gap> IsRecord( TransformingPermutationsCharacterTables(
> res.tblmnG, lib ) );
true
## ./ctocenex.xml (1029-1040)
gap> 3f3p:= CharacterTable( "3.F3+" );;
gap> f3p:= CharacterTable( "F3+" );;
gap> approxfus:= CompositionMaps(
> InverseMap( GetFusionMap( 3f3p, f3p ) ),
> CompositionMaps( GetFusionMap( tblmG, f3p ),
> GetFusionMap( lib, tblmG ) ) );;
gap> poss:= PossibleClassFusions( lib, 3f3p,
> rec( fusionmap:= approxfus ) );;
gap> Length( poss );
1
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> data.replayInterval:= oldinterval;
> fi;
##
gap> STOP_TEST( "ctocenex.tst" );
gap> SizeScreen( save );;
#############################################################################
##
#E
|
