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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Andrew Solomon.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## Conversion to, and fast methods for, transformation representation
## of EndoMappings.
##
############################################################################
##
#R IsTransformationRepOfEndo(<obj>)
##
## An endomorphism of a finite domain <D> with EnumeratorSorted can be
## represented as transformation on [1 .. Length(EnumeratorSorted(D))]
##
DeclareRepresentation("IsTransformationRepOfEndo",
IsComponentObjectRep and IsAttributeStoringRep,
["transformation"]);
############################################################################
##
#F EndoMappingByTransformation(<dom>, <gmfam>, <trans>)
##
## Creates an endo general mapping from <dom> to itself
## in the general mappings family <gmfam>, described by transformation
## <trans>. At present this is a private function.
##
BindGlobal("EndoMappingByTransformation",
function(dom, gmfam, trans)
local tmap;
tmap := Objectify(gmfam!.transtype, rec( transformation := trans));
SetSource(tmap,dom);
SetRange(tmap,dom);
SetIsEndoMapping(tmap, true);
return tmap;
end);
############################################################################
##
#A TransformationRepresentation(<obj>)
##
## The user must deliberately put endomorphisms into this representation
## since it calls enumerator sorted on the Source.
##
InstallMethod(TransformationRepresentation,
"for an endo general mapping", true,
[IsEndoMapping], 0,
function(m)
local trans;
if not (HasIsFinite(Source(m)) and IsFinite(Source(m))) then
TryNextMethod();
fi;
# create the type if necessary
if not IsBound(FamilyObj(m)!.transtype) then
FamilyObj(m)!.transtype := NewType(FamilyObj(m),
IsEndoMapping and IsNonSPGeneralMapping
and IsTransformationRepOfEndo);
fi;
trans:= Transformation(List([1 .. Size(Source(m))],
i -> Position(EnumeratorSorted(Source(m)),
EnumeratorSorted(Source(m))[i]^m)));
return EndoMappingByTransformation(Source(m),FamilyObj(m), trans);
end);
InstallMethod(TransformationRepresentation,
"for an endo general mapping", true,
[IsEndoMapping and IsTransformationRepOfEndo], 0,m->m);
#############################################################################
##
#M CompositionMapping2( <endo>, <endo> ) . . for IsTransformationRepOfEndo
##
## Note: this is the dual of \*
##
InstallMethod(CompositionMapping2,
"IsTransformationRepOfEndo, IsTransformationRepOfEndo", IsIdenticalObj,
[IsTransformationRepOfEndo and IsEndoMapping,
IsTransformationRepOfEndo and IsEndoMapping],
function(n, m)
local mntrans;
if Source(n) <> Source(m) then
TryNextMethod();
fi;
mntrans := m!.transformation* n!.transformation;
return EndoMappingByTransformation(Source(m),FamilyObj(m), mntrans);
end);
InstallMethod( CompositionMapping2,
"IsEndoMapping, IsTransformationRepOfEndo", IsIdenticalObj,
[ IsEndoMapping, IsTransformationRepOfEndo and IsEndoMapping ],
function( n, m )
if Source(n) <> Source(m) then
#T Is this really necessary?
TryNextMethod();
fi;
return EndoMappingByTransformation( Source(m), FamilyObj(m),
m!.transformation
* TransformationRepresentation( n )!.transformation );
end );
InstallMethod( CompositionMapping2,
"IsTransformationRepOfEndo, IsEndoMapping", IsIdenticalObj,
[ IsTransformationRepOfEndo and IsEndoMapping, IsEndoMapping ],
function( n, m )
if Source(n) <> Source(m) then
#T Is this really necessary?
TryNextMethod();
fi;
return EndoMappingByTransformation( Source(m), FamilyObj(m),
TransformationRepresentation( m )!.transformation
* n!.transformation );
end );
#############################################################################
##
#M \=( <endo>, <endo> ) . . . for IsTransformationRepOfEndo
##
InstallMethod(\=,
"IsTransformationRepOfEndo, IsTransformationRepOfEndo", IsIdenticalObj,
[IsTransformationRepOfEndo and IsEndoMapping,
IsTransformationRepOfEndo and IsEndoMapping], 0,
function(m, n)
if Source(n) <> Source(m) then
return false;
fi;
return m!.transformation = n!.transformation;
end);
InstallMethod(\=,
"IsTransformationRepOfEndo, IsEndoMapping", IsIdenticalObj,
[IsTransformationRepOfEndo and IsEndoMapping, IsEndoMapping], 0,
function(m, n)
if Source(n) <> Source(m) then
return false;
fi;
return m!.transformation = TransformationRepresentation(n)!.transformation;
end);
InstallMethod(\=,
"IsEndoMapping, IsTransformationRepOfEndo", IsIdenticalObj,
[IsEndoMapping, IsTransformationRepOfEndo and IsEndoMapping], 0,
function(m, n)
if Source(n) <> Source(m) then
return false;
fi;
return TransformationRepresentation(m)!.transformation = n!.transformation;
end);
#############################################################################
##
#M \<( <endo>, <endo> ) . . . for IsTransformationRepOfEndo
##
InstallMethod(\<,
"IsTransformationRepOfEndo, IsTransformationRepOfEndo", IsIdenticalObj,
[IsEndoMapping and IsTransformationRepOfEndo,
IsEndoMapping and IsTransformationRepOfEndo], 0,
function(m, n)
return TransformationRepresentation(m)!.transformation <
TransformationRepresentation(n)!.transformation;
end);
InstallMethod(\<,
"IsEndoMapping, IsTransformationRepOfEndo", IsIdenticalObj,
[IsEndoMapping, IsEndoMapping and IsTransformationRepOfEndo], 0,
function(m, n)
if Source(n) <> Source(m) then
TryNextMethod();
fi;
if not HasEnumeratorSorted(Source(m)) then
TryNextMethod();
fi;
return TransformationRepresentation(m)!.transformation <
TransformationRepresentation(n)!.transformation;
end);
InstallMethod(\<,
"IsTransformationRepOfEndo, IsEndoMapping", IsIdenticalObj,
[IsEndoMapping and IsTransformationRepOfEndo, IsEndoMapping], 0,
function(m, n)
if Source(n) <> Source(m) then
TryNextMethod();
fi;
if not HasEnumeratorSorted(Source(m)) then
TryNextMethod();
fi;
return TransformationRepresentation(m)!.transformation <
TransformationRepresentation(n)!.transformation;
end);
#############################################################################
##
#M ImagesElm( <endo>, <elm> ) . . . for IsTransformationRepOfEndo
##
InstallMethod( ImagesElm,
"IsTransformationRepOfEndo",
FamSourceEqFamElm,
[IsTransformationRepOfEndo and IsEndoMapping, IsObject ], 0,
function( endo, elm )
local poselm;
poselm := Position(EnumeratorSorted(Source(endo)), elm);
return [EnumeratorSorted(Source(endo))[poselm^(endo!.transformation)]];
end);
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