Lift some functions to magmas in general
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Glen Whitney
parent
cf2bc14423
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1ac424c524
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@ -96,11 +96,12 @@ DeclareOperation( "NormalizedQuasigroupTable", [ IsMatrix ] );
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## CREATING QUASIGROUPS AND LOOPS MANUALLY
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## -------------------------------------------------------------------------
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DeclareAttribute( "CayleyTable", IsQuasigroup );
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DeclareAttribute( "CayleyTable", IsMagma );
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DeclareOperation( "QuasigroupByCayleyTable", [ IsMatrix ] );
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DeclareOperation( "LoopByCayleyTable", [ IsMatrix ] );
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DeclareOperation( "SetQuasigroupElmName", [ IsQuasigroup, IsString ] );
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DeclareSynonym( "SetLoopElmName", SetQuasigroupElmName );
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DeclareAttribute( "ConstructorFromTable", IsMagma );
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DeclareOperation( "CanonicalCopy", [ IsMagma ] );
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#############################################################################
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@ -142,9 +143,9 @@ DeclareOperation( "IntoGroup", [ IsMagma ] );
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## OPPOSITE QUASIGROUPS AND LOOPS
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## --------------------------------------------------------------------------
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DeclareOperation( "OppositeQuasigroup", [ IsQuasigroup ] );
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DeclareOperation( "OppositeLoop", [ IsLoop ] );
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DeclareAttribute( "Opposite", IsQuasigroup );
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DeclareGlobalFunction( "OppositeQuasigroup");
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DeclareGlobalFunction( "OppositeLoop");
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DeclareAttribute( "Opposite", IsMagma );
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#############################################################################
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## AUXILIARY
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@ -149,10 +149,12 @@ end );
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##
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#A CayleyTable( Q )
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##
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## Returns the Cayley table of the quasigroup <Q>
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## Returns the Cayley table of the magma <Q>. This is just like
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## its multiplication table, except in case Q is a submagma of P, in which
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## case the entries used are the indices in P rather than in Q.
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InstallMethod( CayleyTable, "for quasigroup",
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[ IsQuasigroup ],
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InstallMethod( CayleyTable, "for magma",
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[ IsMagma ],
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function( Q )
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local elms, parent_elms;
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elms := Elements( Q );
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@ -194,6 +196,7 @@ function( ct )
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SetAsSSortedList( Q, elms );
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SetParent( Q, Q );
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SetCayleyTable( Q, ct );
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SetConstructorFromTable(QuasigroupByCayleyTable);
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return Q;
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end );
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@ -232,6 +235,7 @@ function( ct )
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SetParent( L, L );
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SetCayleyTable( L, ct );
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SetOne( L, elms[ 1 ] );
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SetConstructorFromTable(LoopByCayleyTable);
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return L;
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end );
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@ -249,22 +253,50 @@ function( Q, name )
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F!.names := name;
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end);
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#############################################################################
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##
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#O ConstructorFromTable( M )
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##
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## Given a magma <M>, returns a function which will create a domain of the
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## same structure as M from from an operation table. This implementation of
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## the method is to backfill the constructors for library domains that do
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## not set the attribute directly at construction time. New domains that wish
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## to use facilities like CanonicalCopy or Opposite should call
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## SetConstructorFromTable at creation time.
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InstallMethod( ConstructorFromTable, "for other magmas",
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[ IsMagma ],
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function ( M )
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# Go in reverse order of refinement of structure
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if IsGroup(M) then
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return GroupByMultiplicationTable;
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elif IsMagmaWithInverses(M) then
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return MagmaWithInversesByMultiplicationTable;
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elif IsMonoid(M) then
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return MonoidByMultiplicationTable;
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elif IsMagmaWithOne(M) then
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return MagmaWithOneByMultiplicationTable;
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elif IsSemigroup(M) then
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return SemigroupByMultiplicationTable;
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fi;
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return MagmaByMultiplicationTable;
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end);
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#############################################################################
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##
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#O CanonicalCopy( Q )
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##
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## Returns a canonical copy of <Q>, that is, an isomorphic object <O> with
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## canonical multiplication table and Parent( <O> ) = <O>.
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## canonical multiplication table and no parent set. Note that this is
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## guaranteed to be a new object, not satisfying IsIdenticalObj with any
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## previously existing structure. THEREFORE:
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## (PROG) Properties and attributes are lost!
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InstallMethod( CanonicalCopy, "for quasigroup or loop",
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[ IsQuasigroup ],
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function( Q )
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if IsLoop( Q ) then
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return LoopByCayleyTable( CayleyTable( Q ) );
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fi;
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return QuasigroupByCayleyTable( CayleyTable( Q ) );
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end);
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InstallMethod( CanonicalCopy, "for magma",
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[ IsMagma ],
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M -> ConstructorFromTable(M)(MultiplicationTable(M));
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);
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#############################################################################
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@ -768,41 +800,31 @@ function( list, dummy )
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##
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#O OppositeQuasigroup( Q )
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##
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## Returns the quasigroup opposite to the quasigroup <Q>.
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## Identical to Opposite, except forces its return to be a quasigroup if
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## possible
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InstallMethod( OppositeQuasigroup, "for quasigroup",
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[ IsQuasigroup ],
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function( Q )
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return QuasigroupByCayleyTable( TransposedMat( CayleyTable( Q ) ) );
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end );
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InstallGlobalFunction( OppositeQuasigroup,
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Q -> IntoQuasigroup( Opposite( L ) ) );
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#############################################################################
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##
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#O OppositeLoop( Q )
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##
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## Returns the loop opposite to the loop <Q>.
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## Identical to Opposite, except forces its return to be a loop if possible
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InstallMethod( OppositeLoop, "for loop",
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[ IsLoop ],
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function( Q )
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return LoopByCayleyTable( TransposedMat( CayleyTable( Q ) ) );
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end );
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InstallGlobalFunction( OppositeLoop, L -> IntoLoop( Opposite( L ) ) );
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#############################################################################
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##
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#A Opposite( Q )
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#A Opposite( M )
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##
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## Returns the quasigroup opposite to the quasigroup <Q>. When
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## <Q> is a loop, a loop is returned.
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## Returns the magma opposite to the magma <M>, with as much structure
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## as can be preserved.
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InstallMethod( Opposite, "for quasigroup",
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[ IsQuasigroup ],
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function( Q )
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if IsLoop( Q ) then
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return LoopByCayleyTable( TransposedMat( CayleyTable( Q ) ) );
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fi;
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return QuasigroupByCayleyTable( TransposedMat( CayleyTable( Q ) ) );
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end );
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InstallMethod( Opposite, "for magma",
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[ IsMagma ],
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M -> ConstructorFromTable(M)( TransposedMat( MultiplicationTable( M ) ) )
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);
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#############################################################################
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## DISPLAYING QUASIGROUPS AND LOOPS
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