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#############################################################################
##
#W equivlist.gd DifSets Package Dylan Peifer
##
## Functions take in a list of difference sets/sums and return a list with
## equivalent sets/sums removed.
##
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##
#F EquivalentFreeListOfDifferenceSets( <G>, <difsets> )
##
## <#GAPDoc Label="EquivalentFreeListOfDifferenceSets">
## <ManSection>
## <Func Name="EquivalentFreeListOfDifferenceSets" Arg="G, difsets"/>
##
## <Description>
## Returns a list of inequivalent difference sets in the group <A>G</A> that
## consists of one representative from each equivalence class found in the
## list <A>difsets</A> of arbitrary difference sets in <A>G</A>.
##
## <Example><![CDATA[
## gap> G := SmallGroup(16, 4);;
## gap> sets := [[8,9,12,13,14,15], [7,8,9,13,15,16], [1,7,10,11,14,15]];;
## gap> EquivalentFreeListOfDifferenceSets(G, sets);
## [ [ 8, 9, 12, 13, 14, 15 ] ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction( "EquivalentFreeListOfDifferenceSets" );
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##
#F TranslateFreeListOfDifferenceSets( <G>, <difsets> )
##
## <#GAPDoc Label="TranslateFreeListOfDifferenceSets">
## <ManSection>
## <Func Name="TranslateFreeListOfDifferenceSets" Arg="G, difsets"/>
##
## <Description>
## Returns a list of translationally inequivalent difference sets in the
## group <A>G</A> that consists of one representative from each
## translational equivalence class found in the list <A>difsets</A> of
## arbitrary difference sets in <A>G</A>.
##
## <Example><![CDATA[
## gap> G := SmallGroup(16, 4);;
## gap> sets := [[8,9,12,13,14,15], [7,8,9,13,15,16], [1,7,10,11,14,15]];;
## gap> TranslateFreeListOfDifferenceSets(G, sets);
## [ [ 8, 9, 12, 13, 14, 15 ], [ 7, 8, 9, 13, 15, 16 ] ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction( "TranslateFreeListOfDifferenceSets" );
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##
#F EquivalentFreeListOfDifferenceSums( <G>, <N>, <difsums> )
##
## <#GAPDoc Label="EquivalentFreeListOfDifferenceSums">
## <ManSection>
## <Func Name="EquivalentFreeListOfDifferenceSums" Arg="G, N, difsums"/>
##
## <Description>
## Returns a list of inequivalent difference sums in the group <A>G</A>
## mod its normal subgroup <A>N</A> that consists of one representative from
## each equivalence class found in the list <A>difsums</A> of arbitrary
## difference sums in <A>G</A> mod <A>N</A>.
##
## <Example><![CDATA[
## gap> G := SmallGroup(16, 4);;
## gap> N := Subgroup(G, [G.1 * G.2 * G.3, G.3, G.4]);;
## gap> EquivalentFreeListOfDifferenceSums(G, N, [[4,2], [2,4]]);
## [ [ 4, 2 ] ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction( "EquivalentFreeListOfDifferenceSums" );
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##
#F TranslateFreeListOfDifferenceSums( <G>, <N>, <difsums> )
##
## <#GAPDoc Label="TranslateFreeListOfDifferenceSums">
## <ManSection>
## <Func Name="TranslateFreeListOfDifferenceSums" Arg="G, N, difsums"/>
##
## <Description>
## Returns a list of translationally inequivalent difference sums in the
## group <A>G</A> mod its normal subgroup <A>N</A> that consists of one
## representative from each translational equivalence class found in the
## list <A>difsums</A> of arbitrary difference sums in <A>G</A> mod
## <A>N</A>.
##
## <Example><![CDATA[
## gap> G := SmallGroup(16, 4);;
## gap> N := Subgroup(G, [G.1 * G.2 * G.3, G.3, G.4]);;
## gap> TranslateFreeListOfDifferenceSums(G, N, [[4,2], [2,4]]);
## [ [ 4, 2 ] ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction( "TranslateFreeListOfDifferenceSums" );
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##
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