# Some random numbers:
Random([1..1000]);
Random([1..1000]);
Random([1..1000]);
# Use random elements in a group:
fi23 := AtlasGroup("Fi23",NrMovedPoints,137632);
PseudoRandom(fi23);
PseudoRandom(fi23);
PseudoRandom(fi23);
s := Stabiliser(fi23,147,OnPoints); time;
Read("compstab.g");
g := Group(GeneratorsOfGroup(fi23));
sgens := ComputeStabiliserMC(g,147,OnPoints,10);; time; 
StabChain(Group(sgens),rec(limit := Size(fi23)/137632)); time;
# Another example: Computing involution centralisers
LoadPackage("recog");
repeat
x := PseudoRandom(g);
o := Order(x);
until IsEvenInt(o);
o;
x := x^(o/2);
Order(x);
c := Centraliser(fi23,x); time;
ic := RECOG.FindInvolutionCentraliser(fi23,x); time;
StabilizerChain(ic); time;
Size(c);
# Another example: Sym(500) acting on 3 sets, estimating orbit sizes:
s := SymmetricGroup(500);
p := [1,2,3];
Binomial(500,3);
pr := ProductReplacer(s);
r := ORB_EstimateOrbitSize(pr,p,OnSets,20,100000,10000);;
r.estimate;
r.lowerbound;
r.upperbound;
s := Group(r.Sgens);
Size(StabilizerChain(s));
last = Factorial(500)/Binomial(500,3);
ri := RecogniseGroup(s);
Size(ri);
last = Factorial(500)/Binomial(500,3);