Quelle gpdaut.gd Sprache: unbekannt

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#W  gpdaut.gd             GAP4 package `groupoids'             Chris Wensley
#W                                                              & Emma Moore

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#P  IsGroupoidAutomorphism( <mor> )
#P  IsGroupoidAutomorphismByGroupAuto( <aut> )
#P  IsGroupoidAutomorphismByObjectPerm( <aut> )
#P  IsGroupoidAutomorphismByRayShifts( <aut> )
#P  IsGroupoidAutomorphismByPiecesPerm( <aut> )
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DeclareSynonym( "IsGroupoidAutomorphism",
    IsGroupoidHomomorphism and IsAutomorphismWithObjects );
DeclareProperty( "IsGroupoidAutomorphismByGroupAuto", IsGroupoidAutomorphism );
DeclareProperty( "IsGroupoidAutomorphismByObjectPerm", IsGroupoidAutomorphism );
DeclareProperty( "IsGroupoidAutomorphismByPiecesPerm", IsGroupoidAutomorphism );
DeclareProperty( "IsGroupoidAutomorphismByRayShifts", IsGroupoidAutomorphism );

InstallTrueMethod(IsGroupoidAutomorphism, IsGroupoidAutomorphismByGroupAuto);
InstallTrueMethod(IsGroupoidAutomorphism, IsGroupoidAutomorphismByObjectPerm);
InstallTrueMethod(IsGroupoidAutomorphism, IsGroupoidAutomorphismByPiecesPerm);
InstallTrueMethod(IsGroupoidAutomorphism, IsGroupoidAutomorphismByRayShifts);

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#O  GroupoidAutomorphismByGroupAutoNC( <gpd>, <auto> )
#O  GroupoidAutomorphismByGroupAuto( <src>, <auto> )
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DeclareOperation( "GroupoidAutomorphismByGroupAutoNC",
    [ IsGroupoid and IsSinglePiece, IsGroupHomomorphism ] );
DeclareOperation( "GroupoidAutomorphismByGroupAuto",
    [ IsGroupoid and IsSinglePiece, IsGroupHomomorphism ] );

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#O  GroupoidAutomorphismByObjectPermNC( <gpd>, <oims> )
#O  GroupoidAutomorphismByObjectPerm( <gpd>, <oims> )
#O  GroupoidAutomorphismByNtupleNC( <gpd>, <L> )
#O  GroupoidAutomorphismByNtuple( <gpd>, <L> )
#O  GroupoidAutomorphismByRayShiftsNC( <gpd>, <rims> )
#O  GroupoidAutomorphismByRayShifts( <gpd>, <rims> )
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DeclareOperation( "GroupoidAutomorphismByObjectPermNC",
    [ IsGroupoid, IsHomogeneousList ] );
DeclareOperation( "GroupoidAutomorphismByObjectPerm",
    [ IsGroupoid, IsHomogeneousList ] );
DeclareOperation( "GroupoidAutomorphismByNtupleNC",
    [ IsGroupoid and IsSinglePiece, IsHomogeneousList ] );
DeclareOperation( "GroupoidAutomorphismByNtuple",
    [ IsGroupoid and IsSinglePiece, IsHomogeneousList ] );
DeclareOperation( "GroupoidAutomorphismByRayShiftsNC",
    [ IsGroupoid and IsSinglePiece, IsHomogeneousList ] );
DeclareOperation( "GroupoidAutomorphismByRayShifts",
    [ IsGroupoid and IsSinglePiece, IsHomogeneousList ] );

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#O  GroupoidInnerAutomorphism( <gpd>, <arr> )
#O  GroupoidInnerAutomorphismNormalSubgroupoid( <gpd>, <nsgpd>, <arr> )
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DeclareOperation( "GroupoidInnerAutomorphism",
    [ IsGroupoid, IsGroupoidElement ] );
DeclareOperation( "GroupoidInnerAutomorphismNormalSubgroupoid",
    [ IsGroupoid, IsGroupoid, IsGroupoidElement ] );

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#P  IsAutomorphismGroupOfGroupoid( <gp> )
#P  IsGroupOfGroupoidAutomorphisms( <gp> )
#A  AutomorphismGroupOfGroupoid( <gpd> )
#O  NiceObjectAutoGroupGroupoid( <gpd>, <aut> )
#A  EmbeddingsInNiceObject( <gp> )
##
DeclareProperty( "IsAutomorphismGroupOfGroupoid", IsGroup );
DeclareProperty( "IsGroupOfGroupoidAutomorphisms", IsGroup );
DeclareAttribute( "AutomorphismGroupOfGroupoid", IsGroupoid );
DeclareOperation( "NiceObjectAutoGroupGroupoid", [ IsGroupoid, IsGroup ] );
DeclareAttribute( "EmbeddingsInNiceObject", IsGroup );

InstallTrueMethod( IsGroup, IsAutomorphismGroupOfGroupoid );
InstallTrueMethod( IsGroup, IsGroupOfGroupoidAutomorphisms );

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#A  AutomorphismGroupoidOfGroupoid( <gpd> )
#A  IsomorphismClassesOfGroupoid( <gpd > )
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DeclareAttribute( "AutomorphismGroupoidOfGroupoid", IsGroupoid );
DeclareAttribute( "IsomorphismClassPositionsOfGroupoid", IsGroupoid );

## ======================================================================== ##
##                Homogeneous discrete groupoid automorphisms               ##
## ======================================================================== ##

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#P  IsAutomorphismOfHomogeneousDiscreteGroupoid( IsGroup )
#O  GroupoidAutomorphismByGroupAutosNC( <gpd, homs> )
#O  GroupoidAutomorphismByGroupAutos( <gpd, homs> )
#T  GroupoidHomomorphismDiscreteType  . . type for homomorphisms of groupoids
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DeclareProperty( "IsAutomorphismOfHomogeneousDiscreteGroupoid",
    IsGroupoidAutomorphism );
InstallTrueMethod(IsGroupoidAutomorphism, IsAutomorphismOfHomogeneousDiscreteGroupoid);

DeclareOperation( "GroupoidAutomorphismByGroupAutos",
    [ IsHomogeneousDiscreteGroupoid, IsHomogeneousList ] );
DeclareOperation( "GroupoidAutomorphismByGroupAutosNC",
    [ IsHomogeneousDiscreteGroupoid, IsHomogeneousList ] );
BindGlobal( "GroupoidHomomorphismDiscreteType",
    NewType( GroupoidHomomorphismFamily,
             IsGroupoidHomomorphismFromHomogeneousDiscreteRep
             and IsGroupoidHomomorphismFromHomogeneousDiscrete ) );

## ======================================================================== ##
##                     Homogeneous groupoid automorphisms                   ##
## ======================================================================== ##

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#O  GroupoidAutomorphismByPiecesPermNC( <gpd>, <perm> )
#O  GroupoidAutomorphismByPiecesPerm( <gpd>, <perm> )
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DeclareOperation( "GroupoidAutomorphismByPiecesPermNC",
    [ IsGroupoid, IsPerm ] );
DeclareOperation( "GroupoidAutomorphismByPiecesPerm",
    [ IsGroupoid, IsPerm ] );

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##                              Groupoid actions.                           ##
## ======================================================================== ##

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#C  IsGroupoidAction( <map> )
#R  IsGroupoidActionRep( <map> )
#A  ActionMap( <act> )
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##  A groupoid action is a mapping which satisfies the conjugation identities
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DeclareCategory( "IsGroupoidAction", IsGeneralMapping );
DeclareRepresentation( "IsGroupoidActionRep",
    IsGroupoidAction and IsAttributeStoringRep,
    [ "Source", "Range", "ActionMap" ] );
DeclareAttribute( "ActionMap", IsGroupoidAction );

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#O  GroupoidActionByConjugation      groupoid G acts on itself by conjugation
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DeclareOperation( "GroupoidActionByConjugation", [ IsGroupoid ] );

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#C  IsGroupoidActionCollection . . . . . . . category of colls of gpd actions
#C  IsGroupoidActionCollColl . . . . . . . . . . . category of colls of colls
#C  IsGroupoidActionCollCollColl . . . . . .  category of colls, colls, colls
#V  GroupoidActionFamily . . . . . . . . . . . .  family for groupoid actions
#T  GroupoidActionType . . . . . . . . . . . . . .  type for groupoid actions
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DeclareCategoryCollections( "IsGroupoidAction" );
DeclareCategoryCollections( "IsGroupoidActionCollection" );
DeclareCategoryCollections( "IsGroupoidActionCollColl" );
BindGlobal( "GroupoidActionFamily",
    NewFamily( "GroupoidActionFamily", IsGroupoidAction,
               CanEasilySortElements, CanEasilySortElements ) );
BindGlobal( "GroupoidActionType",
            NewType( GroupoidActionFamily, IsGroupoidActionRep ) );

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[ Dauer der Verarbeitung: 0.15 Sekunden (vorverarbeitet) ]