> #THE NUMBER OF ATTENDANCE QUESTIONS WERE: 6
> 

;
> #Q1
;
> 
;
> #Find P2*P1 ARE THEY SAME
;
> 
;
> # 1 2 3 4 5     1 2 3 4 5      1 2 3 4 5
;
> #[         ] * [         ] =  [         ]
;
> # 2 1 5 3 4     4 1 2 3 5      3 2 1 5 4
;
> 
;
> #NOT SAME
;
> 
;
> #Q2
;
> 
;
> #EXPLAIN IN YOUR OWN WORDS WHY 
;
> #IF THE ORDER OF pi is k THEN |GG{pi}|=k
;
> 
;
> #since k denotes the order of pi, {e,pi,pi^2,...pi^k=e}, we know GG inputs a pos.  integer n and a set of permutations in {1,..n} outputs the subgroup generated by them, so with the order k, nops(GG{pi}) = k
;
> 
;
> #Q3 
;
> 
;
> #Prove that if H is a subgroup of a GROUP G THEN |G|/|H| IS AN INTEGER
;
> 
;
> #Q4
;
> 
;
> #WHOSE THEOREM IS IT?
;
> 
;
> #Joseph-Louis Lagrange
;
> 
;
> #Q5
;
> 
;
> #GENERATE A RANDOM PERMUTATION OF LENGTH 9 AND BY HAND FIND ITS CYCLE REPRESANTATION
;
> #CHECK IT WITH ptoc(pi)
;
> 
;
> PPP := randperm(9)
PPP := [8, 5, 6, 4, 3, 9, 7, 2, 1]
;
> 
;
> #1->8->2->5->3->6->9, 4, 7
;
> PtoC:=proc(P) local n,StillToDo,L,i,C,L1,T:
> 
> n:=nops(P):
> 
> StillToDo:={seq(i,i=1..n)}:
> 
> #L is a dynamically construcete list of cycles in the permutatib P, we start with the empty list
> #until no one is left
> L:=[]:
> 
> while StillToDo<>{} do
> #we pick the smallest survivor
>  i:=min(op(StillToDo)):
>  #we grab its cycle
>  C:=GrabCycle(P,i):
> 
> # We append C to L
>  L:=[op(L),C]:
> 
> #We update StillToDo by kicking out the members of C
> 
> StillToDo:= StillToDo minus convert(C,set):
> od:
> 
> #So far L is a list of cycles but arranged in a random order
> #Now we arrange them according to the convention that the first (largest) entries are increasing
> #L1 is the list of first (largest) entries of each cycle:
> L1:=[seq(L[i][1],i=1..nops(L))]:
> 
> #We now make a table where T[a] is the cycle that starts with  a
> for i from 1 to nops(L) do
>  T[L[i][1]]:=L[i]:
> od:
> 
> #Now we sort L1
> L1:=sort(L1):
> 
> #Now we rewrite L with the above convention
> [seq(T[L1[i]],i=1..nops(L1))]:
> 
> end:
> 
> 
> #FunT(P): The fundamental transformation
> FunT:=proc(P) local P1,i:
> P1:=PtoC(P):
> [seq(op(P1[i]),i=1..nops(P1))]:
> end:
> GrabCycle:=proc(P,i) local C,j:
> 
> #We view the cycle belnging to i as a list, starting at i
> C:=[i]:
> 
> #We find where i points to, call it j
> j:=P[i]:
> 
> while j<>i do
> #sooner or later we will wind back at i (since the permutation is finite) so we append the new
> #arrivals to the list C and rename j
> C:=[op(C),j]:
> j:=P[j]:
> od:
> 
> #We look at the place where it it is max
> j:=max[index](C):
> 
> #we rewrite the cycle with the largest entry first
> 
> [op(j..nops(C),C),op(1..j-1,C)]:
> 
> end:
> PtoC(PPP)
[[4], [7], [9, 1, 8, 2, 5, 3, 6]]
;
> #SAME
;
> 
;
> #Q6
;
> 
;
> #CHECK THAT THE RANGE OF FunT over all permutations of length 7
;
> #(you can use permute(7)) is the same thing (the set of permutations of length 7)
;
> 
;
> FunT:=proc(P) local P1,i:
> P1:=PtoC(P):
> [seq(op(P1[i]),i=1..nops(P1))]:
> end:
> 
;
> P7 := permute(7)
P7 := [[1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 7, 6], [1, 2, 3, 4, 6, 5, 7], [1, 2, 3, 4, 6, 7, 5], [1, 2, 3, 4, 7, 5, 6], [1, 2, 3, 4, 7, 6, 5], [1, 2, 3, 5, 4, 6, 7], [1, 2, 3, 5, 4, 7, 6], [1, 2, 3, 5, 6, 4, 7], [1, 2, 3, 5, 6, 7, 4], [1, 2, 3, 5, 7, 4, 6], [1, 2, 3, 5, 7, 6, 4], [1, 2, 3, 6, 4, 5, 7], [1, 2, 3, 6, 4, 7, 5], [1, 2, 3, 6, 5, 4, 7], [1, 2, 3, 6, 5, 7, 4], [1, 2, 3, 6, 7, 4, 5], [1, 2, 3, 6, 7, 5, 4], [1, 2, 3, 7, 4, 5, 6], [1, 2, 3, 7, 4, 6, 5], [1, 2, 3, 7, 5, 4, 6], [1, 2, 3, 7, 5, 6, 4], [1, 2, 3, 7, 6, 4, 5], [1, 2, 3, 7, 6, 5, 4], [1, 2, 4, 3, 5, 6, 7], [1, 2, 4, 3, 5, 7, 6], [1, 2, 4, 3, 6, 5, 7], [1, 2, 4, 3, 6, 7, 5], [1, 2, 4, 3, 7, 5, 6], [1, 2, 4, 3, 7, 6, 5], [1, 2, 4, 5, 3, 6, 7], [1, 2, 4, 5, 3, 7, 6], [1, 2, 4, 5, 6, 3, 7], [1, 2, 4, 5, 6, 7, 3], [1, 2, 4, 5, 7, 3, 6], [1, 2, 4, 5, 7, 6, 3], [1, 2, 4, 6, 3, 5, 7], [1, 2, 4, 6, 3, 7, 5], [1, 2, 4, 6, 5, 3, 7], [1, 2, 4, 6, 5, 7, 3], [1, 2, 4, 6, 7, 3, 5], [1, 2, 4, 6, 7, 5, 3], [1, 2, 4, 7, 3, 5, 6], [1, 2, 4, 7, 3, 6, 5], [1, 2, 4, 7, 5, 3, 6], [1, 2, 4, 7, 5, 6, 3], [1, 2, 4, 7, 6, 3, 5], [1, 2, 4, 7, 6, 5, 3], [1, 2, 5, 3, 4, 6, 7], [1, 2, 5, 3, 4, 7, 6], [1, 2, 5, 3, 6, 4, 7], [1, 2, 5, 3, 6, 7, 4], [1, 2, 5, 3, 7, 4, 6], [1, 2, 5, 3, 7, 6, 4], [1, 2, 5, 4, 3, 6, 7], [1, 2, 5, 4, 3, 7, 6], [1, 2, 5, 4, 6, 3, 7], [1, 2, 5, 4, 6, 7, 3], [1, 2, 5, 4, 7, 3, 6], [1, 2, 5, 4, 7, 6, 3], [1, 2, 5, 6, 3, 4, 7], [1, 2, 5, 6, 3, 7, 4], [1, 2, 5, 6, 4, 3, 7], [1, 2, 5, 6, 4, 7, 3], [1, 2, 5, 6, 7, 3, 4], [1, 2, 5, 6, 7, 4, 3], [1, 2, 5, 7, 3, 4, 6], [1, 2, 5, 7, 3, 6, 4], [1, 2, 5, 7, 4, 3, 6], [1, 2, 5, 7, 4, 6, 3], [1, 2, 5, 7, 6, 3, 4], [1, 2, 5, 7, 6, 4, 3], [1, 2, 6, 3, 4, 5, 7], [1, 2, 6, 3, 4, 7, 5], [1, 2, 6, 3, 5, 4, 7], [1, 2, 6, 3, 5, 7, 4], [1, 2, 6, 3, 7, 4, 5], [1, 2, 6, 3, 7, 5, 4], [1, 2, 6, 4, 3, 5, 7], [1, 2, 6, 4, 3, 7, 5], [1, 2, 6, 4, 5, 3, 7], [1, 2, 6, 4, 5, 7, 3], [1, 2, 6, 4, 7, 3, 5], [1, 2, 6, 4, 7, 5, 3], [1, 2, 6, 5, 3, 4, 7], [1, 2, 6, 5, 3, 7, 4], [1, 2, 6, 5, 4, 3, 7], [1, 2, 6, 5, 4, 7, 3], [1, 2, 6, 5, 7, 3, 4], [1, 2, 6, 5, 7, 4, 3], [1, 2, 6, 7, 3, 4, 5], [1, 2, 6, 7, 3, 5, 4], [1, 2, 6, 7, 4, 3, 5], [1, 2, 6, 7, 4, 5, 3], [1, 2, 6, 7, 5, 3, 4], [1, 2, 6, 7, 5, 4, 3], [1, 2, 7, 3, 4, 5, 6], [1, 2, 7, 3, 4, 6, 5], [1, 2, 7, 3, 5, 4, 6], [1, 2, 7, 3, 5, 6, 4], [1, 2, 7, 3, 6, 4, 5], [1, 2, 7, 3, 6, 5, 4], [1, 2, 7, 4, 3, 5, 6], [1, 2, 7, 4, 3, 6, 5], [1, 2, 7, 4, 5, 3, 6], [1, 2, 7, 4, 5, 6, 3], [1, 2, 7, 4, 6, 3, 5], [1, 2, 7, 4, 6, 5, 3], [1, 2, 7, 5, 3, 4, 6], [1, 2, 7, 5, 3, 6, 4], [1, 2, 7, 5, 4, 3, 6], [1, 2, 7, 5, 4, 6, 3], [1, 2, 7, 5, 6, 3, 4], [1, 2, 7, 5, 6, 4, 3], [1, 2, 7, 6, 3, 4, 5], [1, 2, 7, 6, 3, 5, 4], [1, 2, 7, 6, 4, 3, 5], [1, 2, 7, 6, 4, 5, 3], [1, 2, 7, 6, 5, 3, 4], [1, 2, 7, 6, 5, 4, 3], [1, 3, 2, 4, 5, 6, 7], [1, 3, 2, 4, 5, 7, 6], [1, 3, 2, 4, 6, 5, 7], [1, 3, 2, 4, 6, 7, 5], [1, 3, 2, 4, 7, 5, 6], [1, 3, 2, 4, 7, 6, 5], [1, 3, 2, 5, 4, 6, 7], [1, 3, 2, 5, 4, 7, 6], [1, 3, 2, 5, 6, 4, 7], [1, 3, 2, 5, 6, 7, 4], [1, 3, 2, 5, 7, 4, 6], [1, 3, 2, 5, 7, 6, 4], [1, 3, 2, 6, 4, 5, 7], [1, 3, 2, 6, 4, 7, 5], [1, 3, 2, 6, 5, 4, 7], [1, 3, 2, 6, 5, 7, 4], [1, 3, 2, 6, 7, 4, 5], [1, 3, 2, 6, 7, 5, 4], [1, 3, 2, 7, 4, 5, 6], [1, 3, 2, 7, 4, 6, 5], [1, 3, 2, 7, 5, 4, 6], [1, 3, 2, 7, 5, 6, 4], [1, 3, 2, 7, 6, 4, 5], [1, 3, 2, 7, 6, 5, 4], [1, 3, 4, 2, 5, 6, 7], [1, 3, 4, 2, 5, 7, 6], [1, 3, 4, 2, 6, 5, 7], [1, 3, 4, 2, 6, 7, 5], [1, 3, 4, 2, 7, 5, 6], [1, 3, 4, 2, 7, 6, 5], [1, 3, 4, 5, 2, 6, 7], [1, 3, 4, 5, 2, 7, 6], [1, 3, 4, 5, 6, 2, 7], [1, 3, 4, 5, 6, 7, 2], [1, 3, 4, 5, 7, 2, 6], [1, 3, 4, 5, 7, 6, 2], [1, 3, 4, 6, 2, 5, 7], [1, 3, 4, 6, 2, 7, 5], [1, 3, 4, 6, 5, 2, 7], [1, 3, 4, 6, 5, 7, 2], [1, 3, 4, 6, 7, 2, 5], [1, 3, 4, 6, 7, 5, 2], [1, 3, 4, 7, 2, 5, 6], [1, 3, 4, 7, 2, 6, 5], [1, 3, 4, 7, 5, 2, 6], [1, 3, 4, 7, 5, 6, 2], [1, 3, 4, 7, 6, 2, 5], [1, 3, 4, 7, 6, 5, 2], [1, 3, 5, 2, 4, 6, 7], [1, 3, 5, 2, 4, 7, 6], [1, 3, 5, 2, 6, 4, 7], [1, 3, 5, 2, 6, 7, 4], [1, 3, 5, 2, 7, 4, 6], [1, 3, 5, 2, 7, 6, 4], [1, 3, 5, 4, 2, 6, 7], [1, 3, 5, 4, 2, 7, 6], [1, 3, 5, 4, 6, 2, 7], [1, 3, 5, 4, 6, 7, 2], [1, 3, 5, 4, 7, 2, 6], [1, 3, 5, 4, 7, 6, 2], [1, 3, 5, 6, 2, 4, 7], [1, 3, 5, 6, 2, 7, 4], [1, 3, 5, 6, 4, 2, 7], [1, 3, 5, 6, 4, 7, 2], [1, 3, 5, 6, 7, 2, 4], [1, 3, 5, 6, 7, 4, 2], [1, 3, 5, 7, 2, 4, 6], [1, 3, 5, 7, 2, 6, 4], [1, 3, 5, 7, 4, 2, 6], [1, 3, 5, 7, 4, 6, 2], [1, 3, 5, 7, 6, 2, 4], [1, 3, 5, 7, 6, 4, 2], [1, 3, 6, 2, 4, 5, 7], [1, 3, 6, 2, 4, 7, 5], [1, 3, 6, 2, 5, 4, 7], [1, 3, 6, 2, 5, 7, 4], [1, 3, 6, 2, 7, 4, 5], [1, 3, 6, 2, 7, 5, 4], [1, 3, 6, 4, 2, 5, 7], [1, 3, 6, 4, 2, 7, 5], [1, 3, 6, 4, 5, 2, 7], [1, 3, 6, 4, 5, 7, 2], [1, 3, 6, 4, 7, 2, 5], [1, 3, 6, 4, 7, 5, 2], [1, 3, 6, 5, 2, 4, 7], [1, 3, 6, 5, 2, 7, 4], [1, 3, 6, 5, 4, 2, 7], [1, 3, 6, 5, 4, 7, 2], [1, 3, 6, 5, 7, 2, 4], [1, 3, 6, 5, 7, 4, 2], [1, 3, 6, 7, 2, 4, 5], [1, 3, 6, 7, 2, 5, 4], [1, 3, 6, 7, 4, 2, 5], [1, 3, 6, 7, 4, 5, 2], [1, 3, 6, 7, 5, 2, 4], [1, 3, 6, 7, 5, 4, 2], [1, 3, 7, 2, 4, 5, 6], [1, 3, 7, 2, 4, 6, 5], [1, 3, 7, 2, 5, 4, 6], [1, 3, 7, 2, 5, 6, 4], [1, 3, 7, 2, 6, 4, 5], [1, 3, 7, 2, 6, 5, 4], [1, 3, 7, 4, 2, 5, 6], [1, 3, 7, 4, 2, 6, 5], [1, 3, 7, 4, 5, 2, 6], [1, 3, 7, 4, 5, 6, 2], [1, 3, 7, 4, 6, 2, 5], [1, 3, 7, 4, 6, 5, 2], [1, 3, 7, 5, 2, 4, 6], [1, 3, 7, 5, 2, 6, 4], [1, 3, 7, 5, 4, 2, 6], [1, 3, 7, 5, 4, 6, 2], [1, 3, 7, 5, 6, 2, 4], [1, 3, 7, 5, 6, 4, 2], [1, 3, 7, 6, 2, 4, 5], [1, 3, 7, 6, 2, 5, 4], [1, 3, 7, 6, 4, 2, 5], [1, 3, 7, 6, 4, 5, 2], [1, 3, 7, 6, 5, 2, 4], [1, 3, 7, 6, 5, 4, 2], [1, 4, 2, 3, 5, 6, 7], [1, 4, 2, 3, 5, 7, 6], [1, 4, 2, 3, 6, 5, 7], [1, 4, 2, 3, 6, 7, 5], [1, 4, 2, 3, 7, 5, 6], [1, 4, 2, 3, 7, 6, 5], [1, 4, 2, 5, 3, 6, 7], [1, 4, 2, 5, 3, 7, 6], [1, 4, 2, 5, 6, 3, 7], [1, 4, 2, 5, 6, 7, 3], [1, 4, 2, 5, 7, 3, 6], [1, 4, 2, 5, 7, 6, 3], [1, 4, 2, 6, 3, 5, 7], [1, 4, 2, 6, 3, 7, 5], [1, 4, 2, 6, 5, 3, 7], [1, 4, 2, 6, 5, 7, 3], [1, 4, 2, 6, 7, 3, 5], [1, 4, 2, 6, 7, 5, 3], [1, 4, 2, 7, 3, 5, 6], [1, 4, 2, 7, 3, 6, 5], [1, 4, 2, 7, 5, 3, 6], [1, 4, 2, 7, 5, 6, 3], [1, 4, 2, 7, 6, 3, 5], [1, 4, 2, 7, 6, 5, 3], [1, 4, 3, 2, 5, 6, 7], [1, 4, 3, 2, 5, 7, 6], [1, 4, 3, 2, 6, 5, 7], [1, 4, 3, 2, 6, 7, 5], [1, 4, 3, 2, 7, 5, 6], [1, 4, 3, 2, 7, 6, 5], [1, 4, 3, 5, 2, 6, 7], [1, 4, 3, 5, 2, 7, 6], [1, 4, 3, 5, 6, 2, 7], [1, 4, 3, 5, 6, 7, 2], [1, 4, 3, 5, 7, 2, 6], [1, 4, 3, 5, 7, 6, 2], [1, 4, 3, 6, 2, 5, 7], [1, 4, 3, 6, 2, 7, 5], [1, 4, 3, 6, 5, 2, 7], [1, 4, 3, 6, 5, 7, 2], [1, 4, 3, 6, 7, 2, 5], [1, 4, 3, 6, 7, 5, 2], [1, 4, 3, 7, 2, 5, 6], [1, 4, 3, 7, 2, 6, 5], [1, 4, 3, 7, 5, 2, 6], [1, 4, 3, 7, 5, 6, 2], [1, 4, 3, 7, 6, 2, 5], [1, 4, 3, 7, 6, 5, 2], [1, 4, 5, 2, 3, 6, 7], [1, 4, 5, 2, 3, 7, 6], [1, 4, 5, 2, 6, 3, 7], [1, 4, 5, 2, 6, 7, 3], [1, 4, 5, 2, 7, 3, 6], [1, 4, 5, 2, 7, 6, 3], [1, 4, 5, 3, 2, 6, 7], [1, 4, 5, 3, 2, 7, 6], [1, 4, 5, 3, 6, 2, 7], [1, 4, 5, 3, 6, 7, 2], [1, 4, 5, 3, 7, 2, 6], [1, 4, 5, 3, 7, 6, 2], [1, 4, 5, 6, 2, 3, 7], [1, 4, 5, 6, 2, 7, 3], [1, 4, 5, 6, 3, 2, 7], [1, 4, 5, 6, 3, 7, 2], [1, 4, 5, 6, 7, 2, 3], [1, 4, 5, 6, 7, 3, 2], [1, 4, 5, 7, 2, 3, 6], [1, 4, 5, 7, 2, 6, 3], [1, 4, 5, 7, 3, 2, 6], [1, 4, 5, 7, 3, 6, 2], [1, 4, 5, 7, 6, 2, 3], [1, 4, 5, 7, 6, 3, 2], [1, 4, 6, 2, 3, 5, 7], [1, 4, 6, 2, 3, 7, 5], [1, 4, 6, 2, 5, 3, 7], [1, 4, 6, 2, 5, 7, 3], [1, 4, 6, 2, 7, 3, 5], [1, 4, 6, 2, 7, 5, 3], [1, 4, 6, 3, 2, 5, 7], [1, 4, 6, 3, 2, 7, 5], [1, 4, 6, 3, 5, 2, 7], [1, 4, 6, 3, 5, 7, 2], [1, 4, 6, 3, 7, 2, 5], [1, 4, 6, 3, 7, 5, 2], [1, 4, 6, 5, 2, 3, 7], [1, 4, 6, 5, 2, 7, 3], [1, 4, 6, 5, 3, 2, 7], [1, 4, 6, 5, 3, 7, 2], [1, 4, 6, 5, 7, 2, 3], [1, 4, 6, 5, 7, 3, 2], [1, 4, 6, 7, 2, 3, 5], [1, 4, 6, 7, 2, 5, 3], [1, 4, 6, 7, 3, 2, 5], [1, 4, 6, 7, 3, 5, 2], [1, 4, 6, 7, 5, 2, 3], [1, 4, 6, 7, 5, 3, 2], [1, 4, 7, 2, 3, 5, 6], [1, 4, 7, 2, 3, 6, 5], [1, 4, 7, 2, 5, 3, 6], [1, 4, 7, 2, 5, 6, 3], [1, 4, 7, 2, 6, 3, 5], [1, 4, 7, 2, 6, 5, 3], [1, 4, 7, 3, 2, 5, 6], [1, 4, 7, 3, 2, 6, 5], [1, 4, 7, 3, 5, 2, 6], [1, 4, 7, 3, 5, 6, 2], [1, 4, 7, 3, 6, 2, 5], [1, 4, 7, 3, 6, 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1, 5], [7, 4, 6, 2, 3, 5, 1], [7, 4, 6, 2, 5, 1, 3], [7, 4, 6, 2, 5, 3, 1], [7, 4, 6, 3, 1, 2, 5], [7, 4, 6, 3, 1, 5, 2], [7, 4, 6, 3, 2, 1, 5], [7, 4, 6, 3, 2, 5, 1], [7, 4, 6, 3, 5, 1, 2], [7, 4, 6, 3, 5, 2, 1], [7, 4, 6, 5, 1, 2, 3], [7, 4, 6, 5, 1, 3, 2], [7, 4, 6, 5, 2, 1, 3], [7, 4, 6, 5, 2, 3, 1], [7, 4, 6, 5, 3, 1, 2], [7, 4, 6, 5, 3, 2, 1], [7, 5, 1, 2, 3, 4, 6], [7, 5, 1, 2, 3, 6, 4], [7, 5, 1, 2, 4, 3, 6], [7, 5, 1, 2, 4, 6, 3], [7, 5, 1, 2, 6, 3, 4], [7, 5, 1, 2, 6, 4, 3], [7, 5, 1, 3, 2, 4, 6], [7, 5, 1, 3, 2, 6, 4], [7, 5, 1, 3, 4, 2, 6], [7, 5, 1, 3, 4, 6, 2], [7, 5, 1, 3, 6, 2, 4], [7, 5, 1, 3, 6, 4, 2], [7, 5, 1, 4, 2, 3, 6], [7, 5, 1, 4, 2, 6, 3], [7, 5, 1, 4, 3, 2, 6], [7, 5, 1, 4, 3, 6, 2], [7, 5, 1, 4, 6, 2, 3], [7, 5, 1, 4, 6, 3, 2], [7, 5, 1, 6, 2, 3, 4], [7, 5, 1, 6, 2, 4, 3], [7, 5, 1, 6, 3, 2, 4], [7, 5, 1, 6, 3, 4, 2], [7, 5, 1, 6, 4, 2, 3], [7, 5, 1, 6, 4, 3, 2], [7, 5, 2, 1, 3, 4, 6], [7, 5, 2, 1, 3, 6, 4], [7, 5, 2, 1, 4, 3, 6], [7, 5, 2, 1, 4, 6, 3], [7, 5, 2, 1, 6, 3, 4], [7, 5, 2, 1, 6, 4, 3], [7, 5, 2, 3, 1, 4, 6], [7, 5, 2, 3, 1, 6, 4], [7, 5, 2, 3, 4, 1, 6], [7, 5, 2, 3, 4, 6, 1], [7, 5, 2, 3, 6, 1, 4], [7, 5, 2, 3, 6, 4, 1], [7, 5, 2, 4, 1, 3, 6], [7, 5, 2, 4, 1, 6, 3], [7, 5, 2, 4, 3, 1, 6], [7, 5, 2, 4, 3, 6, 1], [7, 5, 2, 4, 6, 1, 3], [7, 5, 2, 4, 6, 3, 1], [7, 5, 2, 6, 1, 3, 4], [7, 5, 2, 6, 1, 4, 3], [7, 5, 2, 6, 3, 1, 4], [7, 5, 2, 6, 3, 4, 1], [7, 5, 2, 6, 4, 1, 3], [7, 5, 2, 6, 4, 3, 1], [7, 5, 3, 1, 2, 4, 6], [7, 5, 3, 1, 2, 6, 4], [7, 5, 3, 1, 4, 2, 6], [7, 5, 3, 1, 4, 6, 2], [7, 5, 3, 1, 6, 2, 4], [7, 5, 3, 1, 6, 4, 2], [7, 5, 3, 2, 1, 4, 6], [7, 5, 3, 2, 1, 6, 4], [7, 5, 3, 2, 4, 1, 6], [7, 5, 3, 2, 4, 6, 1], [7, 5, 3, 2, 6, 1, 4], [7, 5, 3, 2, 6, 4, 1], [7, 5, 3, 4, 1, 2, 6], [7, 5, 3, 4, 1, 6, 2], [7, 5, 3, 4, 2, 1, 6], [7, 5, 3, 4, 2, 6, 1], [7, 5, 3, 4, 6, 1, 2], [7, 5, 3, 4, 6, 2, 1], [7, 5, 3, 6, 1, 2, 4], [7, 5, 3, 6, 1, 4, 2], [7, 5, 3, 6, 2, 1, 4], [7, 5, 3, 6, 2, 4, 1], [7, 5, 3, 6, 4, 1, 2], [7, 5, 3, 6, 4, 2, 1], [7, 5, 4, 1, 2, 3, 6], [7, 5, 4, 1, 2, 6, 3], [7, 5, 4, 1, 3, 2, 6], [7, 5, 4, 1, 3, 6, 2], [7, 5, 4, 1, 6, 2, 3], [7, 5, 4, 1, 6, 3, 2], [7, 5, 4, 2, 1, 3, 6], [7, 5, 4, 2, 1, 6, 3], [7, 5, 4, 2, 3, 1, 6], [7, 5, 4, 2, 3, 6, 1], [7, 5, 4, 2, 6, 1, 3], [7, 5, 4, 2, 6, 3, 1], [7, 5, 4, 3, 1, 2, 6], [7, 5, 4, 3, 1, 6, 2], [7, 5, 4, 3, 2, 1, 6], [7, 5, 4, 3, 2, 6, 1], [7, 5, 4, 3, 6, 1, 2], [7, 5, 4, 3, 6, 2, 1], [7, 5, 4, 6, 1, 2, 3], [7, 5, 4, 6, 1, 3, 2], [7, 5, 4, 6, 2, 1, 3], [7, 5, 4, 6, 2, 3, 1], [7, 5, 4, 6, 3, 1, 2], [7, 5, 4, 6, 3, 2, 1], [7, 5, 6, 1, 2, 3, 4], [7, 5, 6, 1, 2, 4, 3], [7, 5, 6, 1, 3, 2, 4], [7, 5, 6, 1, 3, 4, 2], [7, 5, 6, 1, 4, 2, 3], [7, 5, 6, 1, 4, 3, 2], [7, 5, 6, 2, 1, 3, 4], [7, 5, 6, 2, 1, 4, 3], [7, 5, 6, 2, 3, 1, 4], [7, 5, 6, 2, 3, 4, 1], [7, 5, 6, 2, 4, 1, 3], [7, 5, 6, 2, 4, 3, 1], [7, 5, 6, 3, 1, 2, 4], [7, 5, 6, 3, 1, 4, 2], [7, 5, 6, 3, 2, 1, 4], [7, 5, 6, 3, 2, 4, 1], [7, 5, 6, 3, 4, 1, 2], [7, 5, 6, 3, 4, 2, 1], [7, 5, 6, 4, 1, 2, 3], [7, 5, 6, 4, 1, 3, 2], [7, 5, 6, 4, 2, 1, 3], [7, 5, 6, 4, 2, 3, 1], [7, 5, 6, 4, 3, 1, 2], [7, 5, 6, 4, 3, 2, 1], [7, 6, 1, 2, 3, 4, 5], [7, 6, 1, 2, 3, 5, 4], [7, 6, 1, 2, 4, 3, 5], [7, 6, 1, 2, 4, 5, 3], [7, 6, 1, 2, 5, 3, 4], [7, 6, 1, 2, 5, 4, 3], [7, 6, 1, 3, 2, 4, 5], [7, 6, 1, 3, 2, 5, 4], [7, 6, 1, 3, 4, 2, 5], [7, 6, 1, 3, 4, 5, 2], [7, 6, 1, 3, 5, 2, 4], [7, 6, 1, 3, 5, 4, 2], [7, 6, 1, 4, 2, 3, 5], [7, 6, 1, 4, 2, 5, 3], [7, 6, 1, 4, 3, 2, 5], [7, 6, 1, 4, 3, 5, 2], [7, 6, 1, 4, 5, 2, 3], [7, 6, 1, 4, 5, 3, 2], [7, 6, 1, 5, 2, 3, 4], [7, 6, 1, 5, 2, 4, 3], [7, 6, 1, 5, 3, 2, 4], [7, 6, 1, 5, 3, 4, 2], [7, 6, 1, 5, 4, 2, 3], [7, 6, 1, 5, 4, 3, 2], [7, 6, 2, 1, 3, 4, 5], [7, 6, 2, 1, 3, 5, 4], [7, 6, 2, 1, 4, 3, 5], [7, 6, 2, 1, 4, 5, 3], [7, 6, 2, 1, 5, 3, 4], [7, 6, 2, 1, 5, 4, 3], [7, 6, 2, 3, 1, 4, 5], [7, 6, 2, 3, 1, 5, 4], [7, 6, 2, 3, 4, 1, 5], [7, 6, 2, 3, 4, 5, 1], [7, 6, 2, 3, 5, 1, 4], [7, 6, 2, 3, 5, 4, 1], [7, 6, 2, 4, 1, 3, 5], [7, 6, 2, 4, 1, 5, 3], [7, 6, 2, 4, 3, 1, 5], [7, 6, 2, 4, 3, 5, 1], [7, 6, 2, 4, 5, 1, 3], [7, 6, 2, 4, 5, 3, 1], [7, 6, 2, 5, 1, 3, 4], [7, 6, 2, 5, 1, 4, 3], [7, 6, 2, 5, 3, 1, 4], [7, 6, 2, 5, 3, 4, 1], [7, 6, 2, 5, 4, 1, 3], [7, 6, 2, 5, 4, 3, 1], [7, 6, 3, 1, 2, 4, 5], [7, 6, 3, 1, 2, 5, 4], [7, 6, 3, 1, 4, 2, 5], [7, 6, 3, 1, 4, 5, 2], [7, 6, 3, 1, 5, 2, 4], [7, 6, 3, 1, 5, 4, 2], [7, 6, 3, 2, 1, 4, 5], [7, 6, 3, 2, 1, 5, 4], [7, 6, 3, 2, 4, 1, 5], [7, 6, 3, 2, 4, 5, 1], [7, 6, 3, 2, 5, 1, 4], [7, 6, 3, 2, 5, 4, 1], [7, 6, 3, 4, 1, 2, 5], [7, 6, 3, 4, 1, 5, 2], [7, 6, 3, 4, 2, 1, 5], [7, 6, 3, 4, 2, 5, 1], [7, 6, 3, 4, 5, 1, 2], [7, 6, 3, 4, 5, 2, 1], [7, 6, 3, 5, 1, 2, 4], [7, 6, 3, 5, 1, 4, 2], [7, 6, 3, 5, 2, 1, 4], [7, 6, 3, 5, 2, 4, 1], [7, 6, 3, 5, 4, 1, 2], [7, 6, 3, 5, 4, 2, 1], [7, 6, 4, 1, 2, 3, 5], [7, 6, 4, 1, 2, 5, 3], [7, 6, 4, 1, 3, 2, 5], [7, 6, 4, 1, 3, 5, 2], [7, 6, 4, 1, 5, 2, 3], [7, 6, 4, 1, 5, 3, 2], [7, 6, 4, 2, 1, 3, 5], [7, 6, 4, 2, 1, 5, 3], [7, 6, 4, 2, 3, 1, 5], [7, 6, 4, 2, 3, 5, 1], [7, 6, 4, 2, 5, 1, 3], [7, 6, 4, 2, 5, 3, 1], [7, 6, 4, 3, 1, 2, 5], [7, 6, 4, 3, 1, 5, 2], [7, 6, 4, 3, 2, 1, 5], [7, 6, 4, 3, 2, 5, 1], [7, 6, 4, 3, 5, 1, 2], [7, 6, 4, 3, 5, 2, 1], [7, 6, 4, 5, 1, 2, 3], [7, 6, 4, 5, 1, 3, 2], [7, 6, 4, 5, 2, 1, 3], [7, 6, 4, 5, 2, 3, 1], [7, 6, 4, 5, 3, 1, 2], [7, 6, 4, 5, 3, 2, 1], [7, 6, 5, 1, 2, 3, 4], [7, 6, 5, 1, 2, 4, 3], [7, 6, 5, 1, 3, 2, 4], [7, 6, 5, 1, 3, 4, 2], [7, 6, 5, 1, 4, 2, 3], [7, 6, 5, 1, 4, 3, 2], [7, 6, 5, 2, 1, 3, 4], [7, 6, 5, 2, 1, 4, 3], [7, 6, 5, 2, 3, 1, 4], [7, 6, 5, 2, 3, 4, 1], [7, 6, 5, 2, 4, 1, 3], [7, 6, 5, 2, 4, 3, 1], [7, 6, 5, 3, 1, 2, 4], [7, 6, 5, 3, 1, 4, 2], [7, 6, 5, 3, 2, 1, 4], [7, 6, 5, 3, 2, 4, 1], [7, 6, 5, 3, 4, 1, 2], [7, 6, 5, 3, 4, 2, 1], [7, 6, 5, 4, 1, 2, 3], [7, 6, 5, 4, 1, 3, 2], [7, 6, 5, 4, 2, 1, 3], [7, 6, 5, 4, 2, 3, 1], [7, 6, 5, 4, 3, 1, 2], [7, 6, 5, 4, 3, 2, 1]]
;
> 
;
> FunT([7, 6, 1, 5, 4, 2, 3])
[5, 4, 6, 2, 7, 3, 1]
;
> 
;
> RangeCheck := proc(P) local N,i:
> option remember:
> 
> N := 0:
> for i from 1 to nops(P) do
>     if FunT(P[i]) = P[i] then
>        N := N+1:
>     fi:
> od:
> 
> N:
> end:
> RangeCheck(P7)
21
;
> 
;