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### racks
InstallMethod(Rack, "for a matrix", [ IsMatrix ],
function(matrix)
local fam, obj;
if not IS_RACK(matrix) then
Error("this is not a rack");
fi;
fam := NewFamily("RackElmFamily", IsRackElm, IsMultiplicativeElement);
fam!.DefaultType := NewType(fam, IsRackElmRep);
obj := Objectify(NewType(CollectionsFamily(fam), IsRack and IsAttributeStoringRep), rec());
fam!.Rack := obj;
SetSize(obj, Size(matrix));
SetMatrixOfRack(obj, matrix);
SetPermutations(obj, List([1..Size(obj)], x->PermList(matrix[x])));
return obj;
end);
InstallOtherMethod(Matrix, [ IsRack and HasMatrixOfRack ], MatrixOfRack);
InstallMethod(ViewObj,
"for a rack",
[ IsRack ],
function(obj)
Print("<A rack of size ", Size(obj), ">");
end);
InstallMethod(PrintObj,
"for a rack",
[ IsRack ],
function(obj)
Print( "Rack( ", MatrixOfRack(obj), " )");
end);
InstallMethod(Enumerator,
"for a rack",
[ IsRack ],
AsList);
InstallMethod(AsList,
"for a rack",
[ IsRack ],
function( obj )
return List([1..Size(obj)], x->RackElmConstructor(obj, x));
end);
InstallMethod( \=,
"for two elements of a rack",
IsIdenticalObj, [ IsRackElm, IsRackElm ],
function( x, y )
return x![1] = y![1];
end);
InstallMethod(ViewObj, "for a rack element", [ IsRackElm ],
function(x)
Print("<", x![1], ">");
end);
InstallMethod(RackElmConstructor, "for a rack and an integer", [ IsRack, IsInt ],
function( obj, x )
return Objectify(ElementsFamily(FamilyObj(obj))!.DefaultType, [ x ]);
end);
InstallMethod( \*,
"for two elements of a rack",
IsIdenticalObj, [ IsRackElm, IsRackElm ],
function( x, y )
local fam;
fam := FamilyObj(x);
return RackElmConstructor(fam!.Rack, MatrixOfRack(fam!.Rack)[x![1],y![1]]);
end);
InstallMethod(Rack2YB, "for a rack", [ IsRack ],
function(obj)
return YB(MatrixOfRack(obj), List([1..Size(obj)], x->[1..Size(obj)]));
end);
[ Dauer der Verarbeitung: 0.30 Sekunden
(vorverarbeitet)
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