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##
#W smallest.gd DifSets Package Dylan Peifer
##
## Functions use `SmallestImageSet` from GRAPE package to find the
## lexicographically smallest equivalent difference set to a given set.
##
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##
#F SmallestEquivalentDifferenceSet( <G>, <D> )
##
## <#GAPDoc Label="SmallestEquivalentDifferenceSet">
## <ManSection>
## <Func Name="SmallestEquivalentDifferenceSet" Arg="G, D"/>
##
## <Description>
## Returns the set that is lexicographically smallest among all sets that
## are equivalent to the difference set <A>D</A> in the group <A>G</A>.
##
## <Example><![CDATA[
## gap> G := SmallGroup(16, 4);;
## gap> SmallestEquivalentDifferenceSet(G, [8,9,12,13,14,15]);
## [ 1, 2, 3, 4, 8, 15 ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction( "SmallestEquivalentDifferenceSet" );
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##
#F SmallestEquivalentFreeListOfDifferenceSets( <G>, <difsets> )
##
## <#GAPDoc Label="SmallestEquivalentFreeListOfDifferenceSets">
## <ManSection>
## <Func Name="SmallestEquivalentFreeListOfDifferenceSets" Arg="G, difsets"/>
##
## <Description>
## Returns a list containing the lexicographically smallest set for each set
## in the list of difference sets <A>difsets</A> in the group <A>G</A>.
## Duplicates are removed, so the returned list contains exactly one
## representative from each equivalence class found in <A>difsets</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> SmallestEquivalentFreeListOfDifferenceSets(G, sets);
## [ [ 1, 2, 3, 4, 8, 15 ] ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction( "SmallestEquivalentFreeListOfDifferenceSets" );
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