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#############################################################################
##
#W equivlist.gi DifSets Package Dylan Peifer
##
## Functions take in a list of difference sets/sums and return a list with
## equivalent sets/sums removed.
##
#############################################################################
##
#F EquivalentFreeListOfDifferenceSets( <G>, <difsets> )
##
InstallGlobalFunction( EquivalentFreeListOfDifferenceSets, function (G, difsets)
local v, prod, auts, newdifsets, D, aut, i, d;
# make difsets a set of immutable elements so we can use binary search
# each difset must be a set so that permutations don't matter
Apply(difsets, x->Immutable(Set(x)));
difsets := Set(difsets);
# handle special case of trivial input
if Length(difsets) <= 1 then return difsets; fi;
v := Size(G);
prod := ProductTable(G);
auts := AutomorphismsTable(G);
newdifsets := []; # will store inequivalent difsets
while Length(difsets) > 0 do
# remove a difset and add to the equivalent-free list
D := Remove(difsets);
Add(newdifsets, D);
# remove anything equivalent to D from difsets
for aut in auts do
for i in [1..v] do
d := Set(D, x->prod[i][aut[x]]);
RemoveSet(difsets, d);
od;
od;
od;
return newdifsets;
end );
#############################################################################
##
#F TranslateFreeListOfDifferenceSets( <G>, <difsets> )
##
InstallGlobalFunction( TranslateFreeListOfDifferenceSets, function (G, difsets)
local v, prod, newdifsets, D, i, d;
# make difsets a set of immutable elements so we can use binary search
# each difset must be a set so that permutations don't matter
Apply(difsets, x->Immutable(Set(x)));
difsets := Set(difsets);
# handle special case of trivial input
if Length(difsets) <= 1 then return difsets; fi;
v := Size(G);
prod := ProductTable(G);
newdifsets := []; # will store inequivalent difsets
while Length(difsets) > 0 do
# remove a difset and add to the equivalent-free list
D := Remove(difsets);
Add(newdifsets, D);
# remove anything translationally equivalent to D from difsets
for i in [1..v] do
d := Set(D, x->prod[i][x]);
RemoveSet(difsets, d);
od;
od;
return newdifsets;
end );
#############################################################################
##
#F EquivalentFreeListOfDifferenceSums( <G>, <N>, <difsums> )
##
InstallGlobalFunction( EquivalentFreeListOfDifferenceSums, function (G, N, difsums)
local v, w,prod, auts, newdifsums, S, aut, i, s, j;
# make difsums a set of immutable elements so we can use binary search
Apply(difsums, x->Immutable(x));
difsums := Set(difsums);
# handle special case of trivial input
if Length(difsums) <= 1 then return difsums; fi;
v := Size(G);
w := Size(N);
prod := ProductTable(G/N);
auts := InducedAutomorphismsTable(G, N);
newdifsums := []; # will store inequivalent difsums
while Length(difsums) > 0 do
# remove a difsum and add it to the equivalent-free list
S := Remove(difsums);
Add(newdifsums, S);
# remove anything equivalent to S from difsums
for aut in auts do
for i in [1..v/w] do
s := EmptyPlist(v/w);
for j in [1..v/w] do
s[prod[i][aut[j]]] := S[j];
od;
RemoveSet(difsums, s);
od;
od;
od;
return newdifsums;
end );
#############################################################################
##
#F TranslateFreeListOfDifferenceSums( <G>, <N>, <difsums> )
##
InstallGlobalFunction( TranslateFreeListOfDifferenceSums, function (G, N, difsums)
local v, w, prod, newdifsums, S, i, s, j;
# make difsums a set of immutable elements so we can use binary search
Apply(difsums, x->Immutable(x));
difsums := Set(difsums);
# handle special case of trivial input
if Length(difsums) <= 1 then return difsums; fi;
v := Size(G);
w := Size(N);
prod := ProductTable(G/N);
newdifsums := []; # will store inequivalent difsums
while Length(difsums) > 0 do
# remove a difsum and add it to the equivalent-free list
S := Remove(difsums);
Add(newdifsums, S);
# remove anything equivalent to S from difsums
for i in [1..v/w] do
s := EmptyPlist(v/w);
for j in [1..v/w] do
s[prod[i][j]] := S[j];
od;
RemoveSet(difsums, s);
od;
od;
return newdifsums;
end );
#############################################################################
##
#E
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