> #Attendence Q1: 
> #Find P2*P1. Are they same? 
;
> #P1: 21534; P2: 41235
;
> #P2*P1 = 32154
;
> #Not same as P1*P2
;
> 
;
> 
;
> #Attendence Q2:
> #Explain in your own words, why is the order of pi is k, the |GG(pi)| = k?
;
> #Since we do k times multiplications for pi, so generates k sets in GG, and hence |GG(pi)|=k
;
> 
;
> 
;
> #Attendence Q3: 
> #prove that if H is a subgroup of a group G then 
;
> #|G|/|H| is an integer
;
> 
;
> 
;
> #Attendence Q4:
> #whose theorem is it?
;
> 
;
> 
;
> #Attendence Q5:
> #generate a random permutation of length 9 (use randperm(9))
;
> #and write by hand find its cycle representation. And then check it with PtoC(pi).
;
> with(combinat); pi:= randperm(9);
[Chi, bell, binomial, cartprod, character, choose, composition, conjpart, 
decodepart, encodepart, eulerian1, eulerian2, fibonacci, firstcomb, firstpart,
firstperm, graycode, inttovec, lastcomb, lastpart, lastperm, multinomial, 
nextcomb, nextpart, nextperm, numbcomb, numbcomp, numbpart, numbperm, partition
, permute, powerset, prevcomb, prevpart, prevperm, randcomb, randpart, randperm
, rankcomb, rankperm, setpartition, stirling1, stirling2, subsets, unrankcomb,
unrankperm, vectoint]
Typesetting:-mprintslash([(pi := [8, 5, 6, 4, 3, 9, 7, 2, 1])],[[8, 5, 6, 4, 3,
9, 7, 2, 1]])

;
> #8 5 6 4 3 9 7 2 1
;
> #1->8->2->5->3->6->9->1, 4->4, 7->7
;
> #cycle: (1825369)(4)(7)
;
> #By the maple code .
;
> #PtoC([8, 5, 6, 4, 3, 9, 7, 2, 1])
[[4], [7], [9, 1, 8, 2, 5, 3, 6]]
;
> #Correct. 
;
> 
;
> 
;
> #Attendence Q6:
> #check that the range of FunT over all permutations of length 7
;
> #so the range is 1 to 7
;
> pi:= randperm(7)
Typesetting:-mprintslash([(pi := [6, 2, 1, 7, 4, 3, 5])],[[6, 2, 1, 7, 4, 3, 5]
])

;
> FunT(pi)
[2, 6, 3, 1, 7, 5, 4]
;
> 
;
> 
;
> 
;
> 
;
> 
;
> 
;