//Session file
SetLogFile("fixpntsR.log": Overwrite := true);

// fixed point counter
numFP := function(sd);
   s := 0;
   n := #sd;
   for  i := 1 to n do
        if  i eq sd[i] then s := s+1; end if;
        end for;
   return s;
   end function;

//define deck, set up "shuffle group", sample size
n := 10;
udeck := [1..n];
G := SymmetricGroup(n);
numsamp :=5000;
// remember that udeck^(pi^(-1)) is the deck shuffled by pi

//average number of fixed points
nfp := 0;
for i := 1 to numsamp do
    pi := Random(G);
    nfp := nfp+numFP(udeck^(pi^(-1))); 
    end for;
avgFP := nfp/numsamp;
print "avgFP = ",avgFP;

//probability of a fixed point
fp := 0;
for i := 1 to numsamp do
    pi := Random(G);
    if numFP(udeck^(pi^(-1))) gt 0 then fp := fp+1; end if; 
    end for;
probFP := fp/numsamp;
print "probFP = ",probFP;

//End Session
UnsetLogFile();