#Names:
#Zachary Bridwell
#McKenzie Marquez

#Creating Cosets of Z mod n where n is arbitrary and a subgroup of Z mod n is known.

def CosetofInt(G,H,n):
    Ans=[[mod(G[j]+H[i],n) for i in range(len(H))] for j in range(len(G))]
    ans=[]
    for k in range(len(Ans)):
        ans=ans+[Ans[k]]
    return ans

def Index(G,H):
    return len(G)/len(H)

G=range(15) #Z mod 15
H=[0,5,10] #Subgroup of G generated by 5
CosetofInt(G,H,len(G))
#Note that if converted to "Set" notation, will return Z mod 15 (Not the union of each element to eliminate duplicates).
#The problem with this is that we have repeating subgroups. Ie. [0,5,10]=[5,10,0] in Group Theory

def NicePrint(alist):
    print "Since Z mod n is abelian, H is a normal subgroup."
    for i in range(Index(G,H)):
        print "The %s + H coset is:"%G[i]
        print "%s." %(alist[i])
    return None

NicePrint(CosetofInt(G,H,15))

G=range(21) #Z mod 21
H=[0,7,14] #Subgroup generated by 7
NicePrint(CosetofInt(G,H,len(G)))

NicePrint(CosetofInt(range(100),[5*i for i in range(100/5)],len(range(100))))
#Note that the only problem with entering it this way is that we get the Coset 6+H=1+H, 5+H; so there is an extra element.