GAP Manual: 51.21. TestConsistencyMaps

TestConsistencyMaps( powmap1, fusmap, powmap2 )
TestConsistencyMaps( powmap1, fusmap, powmap2, fus_imp )

Like in TransferDiagram, it is checked that parametrized maps (see chapter Maps and Parametrized Maps) commute:

For all positions i where both powmap1[i] and powmap2[i] are bound, [ CompositionMaps( fusmap, powmap1[i] ) = CompositionMaps( powmap2[i], fusmap ) ] shall hold, so fusmap occurs in diagrams for all considered elements of powmap1 resp. powmap2, and it occurs twice in each diagram.

If a set fus_imp is specified, only those diagrams with elements of fus_imp as preimages of fusmap are considered.

TestConsistencyMaps stores all found improvements in fusmap and elements of powmap1 and powmap2. When an inconsistency occurs, the program immediately returns false; otherwise true is returned.

TestConsistencyMaps stops if no more improvements of fusmap are possible. E.g. if fusmap was unique from the beginning, the powermaps will not be improved. To transfer powermaps by fusions, use TransferDiagram TransferDiagram.

    gap> s:= CharTable( "2F4(2)" );; ru:= CharTable( "Ru" );;
    gap> fus:= InitFusion( s, ru );;
    gap> permchar:= Sum( Sublist( ru.irreducibles, [ 1, 5, 6 ] ) );;
    gap> CheckPermChar( s, ru, fus, permchar );; fus;
    [ 1, 2, 2, 4, 5, 7, 8, 9, 11, 14, 14, [ 13, 15 ], 16, [ 18, 19 ], 20, 
      [ 25, 26 ], [ 25, 26 ], 5, 5, 6, 8, 14, [ 13, 15 ], [ 18, 19 ],
      [ 18, 19 ], [ 25, 26 ], [ 25, 26 ], 27, 27 ]
    gap> TestConsistencyMaps( s.powermap, fus, ru.powermap );
    true
    gap> fus;
    [ 1, 2, 2, 4, 5, 7, 8, 9, 11, 14, 14, 15, 16, 18, 20, [ 25, 26 ],
      [ 25, 26 ], 5, 5, 6, 8, 14, 13, 19, 19, [ 25, 26 ], [ 25, 26 ], 27,
      27 ]
    gap> Indeterminateness( fus );
    16

TestConsistencyMaps is used by SubgroupFusions SubgroupFusions.