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#############################################################################
##
#F RandomClosure( <G>, <fam>, <e> )
##
## <G>: group the nearring is acting on as a transformation nearring
## <fam>: the family of the elements of the nearring
## <e>: a record with the components
## p : the result has probability 1/p to be incorrect
## size : if the size of the nearring is known it can
## be given to the function which produces a
## correct result in this case
##
## Note: only one of p and size has to be set via the function
## SetErrorProbability
RandomClosure := function ( group, fam, e )
local i, m, badp, p, size, addGens;
if IsBound( e.size ) then
size := e.size;
p := 10^100;
else
size := Size(fam!.group)^Size(fam!.group);
p := e.p;
fi;
Info( InfoNearRing, 2, "actual size: ",Size(group) );
addGens := GeneratorsOfGroup( group );
i := 0;
badp := Length(addGens)/(Length(addGens)-1);
while badp^i < p and Size(group) < size do
# Print("->",QuotientRemainder(NumeratorRat(badp^i),DenominatorRat(badp^i))[1],"\n");
i := i + 1;
Info( InfoNearRing, 2, "pass: ", i );
m := GroupElementRepOfNearRingElement(
NearRingElementByGroupRep( fam, Random(group) ) *
NearRingElementByGroupRep( fam, Random( GeneratorsOfGroup(group) ) )
);
if not m in group then
return RandomClosure( ClosureGroup( group, m ), fam, e );
fi;
od;
return group;
end;
#############################################################################
##
#M GroupReduct( <TfmNR> ) random method
##
InstallMethod(
GroupReduct,
"random",
true,
[IsNearRing and IsTransformationNearRing and HasErrorProbability],
0,
function ( nr )
local addGroup, id;
if ErrorProbability( nr ) = 0 then
TryNextMethod();
fi;
id := GroupElementRepOfNearRingElement( GeneratorsOfNearRing(nr)[1] )^0;
addGroup := Group( List( GeneratorsOfNearRing(nr), GroupElementRepOfNearRingElement ), id );
return RandomClosure( addGroup, nr!.elementsInfo, ErrorProbability( nr ) );
end );
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