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############################################################################
##
#W gpdgraph.gd GAP4 package `groupoids' Chris Wensley
#W & Emma Moore
#############################################################################
##
#C IsGraphOfGroupoids( <gg> )
#R IsGraphOfGroupoidsRep( <gg> )
#V GraphOfGroupoidsFamily
#T GraphOfGroupoidsType
##
## A FpWeightedDigraph of groupoids is a 4-tuple containing
## - a FpWeightedDigraph,
## - groups associated with each vertex,
## - subgroupoid associated to tail vertex of each edge, and
## - an isomorphism associated to each edge.
##
DeclareCategory( "IsGraphOfGroupoids", IsGroupoidDigraph );
DeclareRepresentation( "IsGraphOfGroupoidsRep",
IsStructuredDigraph and IsAttributeStoringRep and IsComponentObjectRep,
[ "DigraphOfGraphOfGroupoids", "GroupoidsOfGraphOfGroupoids",
"SubgroupoidsOfGraphOfGroupoids", "IsomorphismsOfGraphOfGroupoids" ] );
BindGlobal( "GraphOfGroupoidsFamily",
NewFamily( "GraphOfGroupoidsFamily", IsGraphOfGroupoids ) );
BindGlobal( "GraphOfGroupoidsType",
NewType( GraphOfGroupoidsFamily, IsGraphOfGroupoidsRep ) );
##############################################################################
##
#P IsGraphOfPermGroupoids( <gg> )
##
DeclareProperty( "IsGraphOfPermGroupoids", IsGraphOfGroupoids );
##############################################################################
##
#P IsGraphOfFpGroupoids( <gg> )
#P IsGraphOfPcGroupoids( <gg> )
##
DeclareProperty( "IsGraphOfFpGroupoids", IsGraphOfGroupoids );
DeclareProperty( "IsGraphOfPcGroupoids", IsGraphOfGroupoids );
#############################################################################
##
#O GraphOfGroupoidsNC( <dig>, <gps>, <subgps>, <isos> )
#O GraphOfGroupoids( <dig>, <gpds>, <subgpds>, <isos> )
##
DeclareOperation( "GraphOfGroupoidsNC",
[ IsFpWeightedDigraph, IsList, IsList, IsList ] );
DeclareOperation( "GraphOfGroupoids",
[ IsFpWeightedDigraph, IsList, IsList, IsList ] );
#############################################################################
##
#A GroupoidsOfGraphOfGroupoids( <gg> )
#A DigraphOfGraphOfGroupoids( <gg> )
#A SubgroupoidsOfGraphOfGroupoids( <gg> )
#A IsomorphismsOfGraphOfGroupoids( <gg> )
##
DeclareAttribute( "GroupoidsOfGraphOfGroupoids", IsGraphOfGroupoids );
DeclareAttribute( "DigraphOfGraphOfGroupoids", IsGraphOfGroupoids );
DeclareAttribute( "SubgroupoidsOfGraphOfGroupoids", IsGraphOfGroupoids );
DeclareAttribute( "IsomorphismsOfGraphOfGroupoids", IsGraphOfGroupoids );
#############################################################################
##
#O NormalFormKBRWS( <groupoid>, <word> )
##
## DeclareOperation( "NormalFormKBRWS", [ IsFpGroupoid, IsObject ] );
#############################################################################
##
#A RightTransversalsOfGraphOfGroupoids( <gg> )
#A LeftTransversalsOfGraphOfGroupoids( <gg> )
##
DeclareAttribute( "RightTransversalsOfGraphOfGroupoids", IsGraphOfGroupoids );
DeclareAttribute( "LeftTransversalsOfGraphOfGroupoids", IsGraphOfGroupoids );
######################################### ####################################
##
#R IsGraphOfGroupoidsWordRep( <ggword> )
#V IsGraphOfGroupoidsWordFamily( <ggword> )
#T IsGraphOfGroupoidsWordType( <ggword> )
##
## A GraphOfGroupoidsWord is a word made from elements in the groupoid
## and edges in the digraph
##
DeclareRepresentation( "IsGraphOfGroupoidsWordRep",
IsObject and IsAttributeStoringRep and IsComponentObjectRep,
[ "GraphOfGroupoidsOfWord",
"TailOfGraphOfGroupsWord", "WordOfGraphOfGroupoidsWord" ] );
BindGlobal( "IsGraphOfGroupoidsWordFamily",
NewFamily( "IsGraphOfGroupoidsWordFamily",
IsGraphOfGroupoidsWordRep ) );
BindGlobal( "IsGraphOfGroupoidsWordType",
NewType( IsGraphOfGroupoidsWordFamily,
IsGraphOfGroupoidsWordRep ) );
######################################### ####################################
##
#P IsGraphOfGroupoidsWord( <ggword> )
#P IsReducedGraphOfGroupoidsWord( <ggword> )
## A GraphOfGroupoidsWord is Reduced if of the form [ t, h, t, h, ..., t, g ]
##
DeclareProperty( "IsGraphOfGroupoidsWord", IsGraphOfGroupoidsWordRep );
DeclareProperty( "IsReducedGraphOfGroupoidsWord", IsGraphOfGroupoidsWord );
#############################################################################
##
#O GraphOfGroupoidsWordNC( <gg>, <tv>, <wL> )
#O GraphOfGroupoidsWord( <gg>, <tv>, <wL> )
##
DeclareOperation( "GraphOfGroupoidsWordNC",
[ IsGraphOfGroupoids, IsInt, IsList ] );
DeclareOperation( "GraphOfGroupoidsWord",
[ IsGraphOfGroupoids, IsInt, IsList ] );
#############################################################################
##
#A GraphOfGroupoidsOfWord( <ggword> )
#A WordOfGraphOfGroupoidsWord( <ggword> )
#O ReducedGraphOfGroupoidsWord( <ggword> )
##
DeclareAttribute( "GraphOfGroupoidsOfWord", IsGraphOfGroupoidsWordRep );
DeclareAttribute( "WordOfGraphOfGroupoidsWord", IsGraphOfGroupoidsWordRep);
DeclareOperation( "ReducedGraphOfGroupoidsWord",
[ IsGraphOfGroupoidsWordRep ] );
#############################################################################
##
#P IsGraphOfGroupoidsGroupoid( <gpd> )
#O GraphOfGroupoidsGroupoid( <gg> )
##
DeclareOperation( "IsGraphOfGroupoidsGroupoid", [ IsGroupoid ] );
DeclareOperation( "GraphOfGroupoidsGroupoid", [ IsGraphOfGroupoids ] );
[ Dauer der Verarbeitung: 0.17 Sekunden
(vorverarbeitet)
]
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