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# This Module is part of the GAP package MAPCLAss
# It contains functions for suggesting, saving and manipulating the collection
# of random tuples in use.
#
# A. James, K. Magaard, S. Shpectorov 2011
#
#
# function inserting a human-suggested tuple
#
InstallGlobalFunction(SuggestTuple,function(tu, PrincipalFiniteGroup, PrincipalTuple, OurG, OurR)
local i, NumberOfGenerators;
NumberOfGenerators:= 2*OurG + OurR;
for i in [1..OurR] do
if not IsConjugate(PrincipalFiniteGroup,tu[2*OurG+i],
PrincipalTuple[i]) then
Print("\n\nTuple cannot be accepted. Element ", i, " is not conjugate\n\n");
return false;
fi;
od;
if Product([1..OurG],x->Comm(tu[2*x-1],tu[2*x]))*
Product(tu{[2*OurG+1..NumberOfGenerators]})<>
One(PrincipalFiniteGroup) then
Print("\n\nTuple cannot be accepted!!\n\n");
return false;
fi;
return rec(tuple:=ShallowCopy(tu),subgroupNumber:=1);
end);
#
# Select a random tuple in a random subgroup
#
InstallGlobalFunction(RandomSubgroupTuple,function(OurG,OurR,SubgroupRecord)
local r,i,s,T,p,c,x, TotalWeight, SmallSubgroups;
SmallSubgroups:=SubgroupRecord.SmallSubgroups;
r:=RandomList([1..SubgroupRecord.TotalWeight]);
for i in [1..Length(SmallSubgroups)] do
s:=SmallSubgroups[i];
if s.weight<r then
r:=r-s.weight;
else
while true do
T:=List([1..2*OurG],x->Random(s.subgroup));
p:=Product([1..OurG],x->Comm(T[x],T[OurG+x]),One(s.subgroup));
if OurR=0 then
if p=One(s.subgroup) then
return rec(tuple:=T,subgroupNumber:=i);
fi;
else
if OurR>1 then
for c in s.classes{[1..OurR-1]} do
Append(T,[RandomList(c)^Random(s.subgroup)]);
od;
p:=p*Product(T{[2*OurG+1..Length(T)]});
fi;
p:=p^-1;
c:=s.classes[OurR];
for x in c do
if IsConjugate(s.subgroup,p,x) then
Append(T,[p]);
return rec(tuple:=T,subgroupNumber:=i);
fi;
od;
fi;
od;
fi;
od;
end);
#
# RandomGeneratingTuple
#
InstallGlobalFunction(RandomGeneratingTuple,function(group, tuple, OurG, OurR)
local i, k, t, product, c;
while true do
t:=List([1..2*OurG], x-> Random(group));
product:=Product([1..OurG], x->Comm(t[x], t[OurG+x]),One(group));
if OurR=0 then
if product=One(group) then
return rec(tuple:=t, subgroupNumber:=1);
fi;
else
if OurR>1 then
for c in tuple{[1..OurR-1]} do
Append(t, [c^Random(group)]);
od;
product:=product*Product(t{[2*OurG+1..Length(t)]});
fi;
if IsConjugate(group, product^-1, tuple[OurR]) then
Append(t,[product^-1]);
if Size(Subgroup(group,t))= Size(group) then
return rec(tuple:=t, subgroupNumber:=1);
fi;
fi;
fi;
od;
end);
#
# Function collecting random tuples
#
InstallGlobalFunction(CollectRandomTuples,function( NumberOfRandomTuples, OurG,
OurR, SubgroupRecord)
local tuples, IsSilent;
tuples:=[];
MaybePrint( [],
["\c\r Collecting Random tuples\c\r"],
["\n\nCollecting ",NumberOfRandomTuples," random tuples...\c\r"]);
while Length(tuples)<NumberOfRandomTuples do
Append(tuples,[RandomSubgroupTuple(OurG, OurR,
SubgroupRecord)]);
od;
MaybePrint([], [], " done\n");
return tuples;
end);
#
# Function collecting only generating tuples
#
InstallGlobalFunction(CollectRandomGeneratingTuples,function(NumberOfRandomTuples,
OurG, OurR, SubgroupRecord, group, tuple)
local tuples, IsSilent;
tuples:=[];
MaybePrint([],[],
["\n\nCollecting ", NumberOfRandomTuples, " generating tuples ..\c"]);
while Length(tuples)<NumberOfRandomTuples do
Append(tuples,[RandomGeneratingTuple(group, tuple, OurG, OurR)]);
od;
MaybePrint([],[], [" done\n"]);
return tuples;
end);
#
# Two routines cleaning the list of random tuples
#
InstallGlobalFunction(CleanCurrent,function(RandomTuples, Orb, SubgroupRecord)
local i,l,s,k, IsSilent;
MaybePrint([],
["\c\rCleaning a list of ", Length(RandomTuples), " tuples\c\r"],
["\rCleaning a list of ", Length(RandomTuples), " tuples\n"]);
# Clear the line
ClearLine();
for i in [1..Length(RandomTuples)] do
l:=Length(Orb.TupleTable);
if IsAbelian(Orb.PrincipalFiniteGroup) then
s:=RandomTuples[i].tuple;
else
# Dont't need to minimize if using Fingerprinting
# TODO: If using quick minimization then do here.
if Orb.FingerPrinting = true then
s:=RandomTuples[i].tuple;
else
s:=MinimizeTuple(RandomTuples[i].tuple, Orb.MinimizationTree,
Orb.MinimumSet, Orb.NumberOfGenerators);
fi;
fi;
# Method selection
if Orb.FingerPrinting = true then
k:=LookUpTupleFP(s,Orb.fprecord, Orb, Orb.TupleTable);
else
k:=LookUpTuple(s, Orb.PrimeCode, Orb.HashLength, Orb.TupleTable,
Orb.Hash, Orb.OurN);
fi;
if not k =fail then
s:=SubgroupRecord.SmallSubgroups[RandomTuples[i].subgroupNumber];
SubgroupRecord.TotalWeight:=SubgroupRecord.TotalWeight-s.weight;
s.weight:=MaximumList([SubgroupRecord.MinimumWeight,
s.weight-SubgroupRecord.KnockDown]);
SubgroupRecord.TotalWeight:= SubgroupRecord.TotalWeight+s.weight;
Unbind(RandomTuples[i]);
fi;
od;
RandomTuples:=Filtered(RandomTuples,x->IsBound(x));
MaybePrint([], [], ["Random Tuples Remaining: ", Length(RandomTuples), "\n"]);
return RandomTuples;
end);
# Call with FingerPrinting and fprecord = false if don't wish to use
# fingerprinting
InstallGlobalFunction(CleanAll,function(RandomTuples, orbits, SubgroupRecord)
local i,Orb, IsSilent;
for i in [1..Length(orbits)] do
MaybePrint([],
[] ,
["\rCleaning orbit ",i,"\c\r"]);
Orb:=orbits[i];
RandomTuples:=CleanCurrent(RandomTuples, Orb, SubgroupRecord);
od;
MaybePrint([],
[],
["\rCleaning done; ",Length(RandomTuples)," random tuples remaining\n"]);
return RandomTuples;
end);
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