Have to cut many other methods down to be more specific to element reps
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@ -30,14 +30,14 @@ end );
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InstallMethod( \=, "for two elements of a quasigroup",
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IsIdenticalObj,
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[ IsQuasigroupElement, IsQuasigroupElement ],
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[ IsQuasigroupElmRep, IsQuasigroupElmRep ],
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function( x, y )
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return FamilyObj( x ) = FamilyObj( y ) and x![ 1 ] = y![ 1 ];
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end );
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InstallMethod( \<, "for two elements of a quasigroup",
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IsIdenticalObj,
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[ IsQuasigroupElement, IsQuasigroupElement ],
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[ IsQuasigroupElmRep, IsQuasigroupElmRrep ],
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function( x, y )
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return FamilyObj( x ) = FamilyObj( y ) and x![ 1 ] < y![ 1 ];
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end );
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@ -57,7 +57,7 @@ end );
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## i.e., a*b*c=(a*b)*c. Powers use binary decomposition.
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InstallMethod( \*, "for two quasigroup elements",
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IsIdenticalObj,
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[ IsQuasigroupElement, IsQuasigroupElement ],
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[ IsQuasigroupElmRep, IsQuasigroupElmRep ],
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function( x, y )
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local F;
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F := FamilyObj( x );
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@ -65,13 +65,13 @@ function( x, y )
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end );
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InstallOtherMethod( \*, "for a QuasigroupElement and a list",
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[ IsQuasigroupElement , IsList ],
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[ IsQuasigroupElmRep , IsList ],
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function( x, ly )
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return List( ly, y -> x*y );
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end );
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InstallOtherMethod( \*, "for a list and a QuasigroupElement",
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[ IsList, IsQuasigroupElement ],
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[ IsList, IsQuasigroupElmRep ],
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function( lx, y )
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return List( lx, x -> x*y );
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end );
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@ -83,7 +83,7 @@ end );
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## z=x/y means zy=x
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InstallMethod( RightDivision, "for two quasigroup elements",
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IsIdenticalObj,
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[ IsQuasigroupElement, IsQuasigroupElement ],
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[ IsQuasigroupElmRep, IsQuasigroupElmRep ],
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function( x, y )
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local F, ycol;
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F := FamilyObj( x );
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@ -93,7 +93,7 @@ end );
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InstallOtherMethod( RightDivision,
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"for a list and a quasigroup element",
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[ IsList, IsQuasigroupElement ],
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[ IsList, IsQuasigroupElmRep ],
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0,
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function( lx, y )
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return List( lx, x -> RightDivision(x, y) );
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@ -101,7 +101,7 @@ end );
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InstallOtherMethod( RightDivision,
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"for a quasigroup element and a list",
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[ IsQuasigroupElement, IsList ],
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[ IsQuasigroupElmRep, IsList ],
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0,
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function( x, ly )
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return List( ly, y -> RightDivision(x, y) );
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@ -110,7 +110,7 @@ end );
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InstallOtherMethod( \/,
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"for two elements of a quasigroup",
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IsIdenticalObj,
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[ IsQuasigroupElement, IsQuasigroupElement ],
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[ IsQuasigroupElmRep, IsQuasigroupElmRep ],
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0,
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function( x, y )
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return RightDivision( x, y );
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@ -118,7 +118,7 @@ end );
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InstallOtherMethod( \/,
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"for a list and a quasigroup element",
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[ IsList, IsQuasigroupElement ],
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[ IsList, IsQuasigroupElmRep ],
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0,
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function( lx, y )
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return List( lx, x -> RightDivision(x, y) );
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@ -126,7 +126,7 @@ end );
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InstallOtherMethod( \/,
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"for a quasigroup element and a list",
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[ IsQuasigroupElement, IsList ],
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[ IsQuasigroupElmRep, IsList ],
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0,
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function( x, ly )
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return List( ly, y -> RightDivision(x, y) );
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@ -135,7 +135,7 @@ end );
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## z = x\y means xz=y
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InstallMethod( LeftDivision, "for two quasigroup elements",
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IsIdenticalObj,
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[ IsQuasigroupElement, IsQuasigroupElement ],
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[ IsQuasigroupElmRep, IsQuasigroupElmRep ],
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function( x, y )
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local F;
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F := FamilyObj( x );
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@ -144,7 +144,7 @@ end );
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InstallOtherMethod( LeftDivision,
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"for a list and a quasigroup element",
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[ IsList, IsQuasigroupElement ],
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[ IsList, IsQuasigroupElmRep ],
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0,
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function( lx, y )
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return List( lx, x -> LeftDivision(x, y) );
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@ -152,7 +152,7 @@ end );
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InstallOtherMethod( LeftDivision,
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"for a quasigroup element and a list",
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[ IsQuasigroupElement, IsList ],
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[ IsQuasigroupElmRep, IsList ],
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0,
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function( x, ly )
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return List( ly, y -> LeftDivision(x, y) );
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@ -215,7 +215,7 @@ end );
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## -------------------------------------------------------------------------
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InstallMethod( \^, "for a quasigroup element and a permutation",
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[ IsQuasigroupElement, IsPerm ],
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[ IsQuasigroupElmRep, IsPerm ],
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function( x, p )
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local F;
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F := FamilyObj( x );
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@ -223,7 +223,7 @@ function( x, p )
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end );
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InstallMethod( OneOp, "for loop elements",
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[ IsLoopElement ],
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[ IsLoopElmRep ],
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function( x )
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local F;
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F := FamilyObj( x );
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@ -237,7 +237,7 @@ end );
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## If <x> is a loop element, returns the left inverse of <x>
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InstallMethod( LeftInverse, "for loop elements",
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[ IsLoopElement ],
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[ IsLoopElmRep ],
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x -> RightDivision( One( x ), x )
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);
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@ -248,12 +248,12 @@ InstallMethod( LeftInverse, "for loop elements",
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## If <x> is a loop element, returns the left inverse of <x>
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InstallMethod( RightInverse, "for loop elements",
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[ IsLoopElement ],
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[ IsLoopElmRep ],
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x -> LeftDivision( x, One( x ) )
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);
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InstallMethod( InverseOp, "for loop elements",
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[ IsLoopElement ],
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[ IsLoopElmRep ],
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function( x )
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local y;
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y := RightInverse( x );
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@ -274,7 +274,7 @@ end );
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## (xy)z = (x(yz))u.
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InstallMethod( Associator, "for three quasigroup elements",
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[ IsQuasigroupElement, IsQuasigroupElement, IsQuasigroupElement ],
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[ IsQuasigroupElmRep, IsQuasigroupElmRep, IsQuasigroupElmRep ],
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function( x, y, z )
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return LeftDivision( x*(y*z), (x*y)*z );
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end);
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@ -288,7 +288,7 @@ end);
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## (xy) = (yx)u.
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InstallMethod( Commutator, "for two quasigroup elements",
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[ IsQuasigroupElement, IsQuasigroupElement ],
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[ IsQuasigroupElmRep, IsQuasigroupElmRep ],
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function( x, y )
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return LeftDivision( y*x, x*y );
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end);
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