[Tutor] checking within a table for identity

[Julieta Rangel]

As some of you might remember, I was trying to figure out how to check for 
associativity within a set.  By taking bits and pieces from you all's 
advice, I put together the following:

import string
def getCayleyTable(op,set):
    product = {}
    for x in set:
        for y in set:
            prompt = "%s %s %s = ? "%(x,op,y)
            print " "
            z = raw_input(prompt)
            product [x,y] = z
            if z not in set:
                print " "
                print "No need to go any further:  your set is not a group"
          	return product
   		print " "
    items = product.items()
    items.sort()

    return product

    print " "

def cross(set1,set2):
    resulting_set = []
    for s1 in set1:
        for s2 in set2:
            resulting_set.append( (s1, s2) )
    return resulting_set

set = raw_input("Enter the elements of the set separated by a comma,ie, 
a,b,c: ")
set = string.split(set, ",")

print " "
op = raw_input("Enter the binary operator sign, ie, * : ")

d = getCayleyTable( op,set )
print " "

m=cross(set,set)
v=[]
for x in m:
    v.append(d[x])
print v

for x in set:
    c= cross(set,v)
    e= cross(v,set)
l=[]
for x in c:
    l.append(d[x])

k=[]
for x in e:
    k.append(d[x])

if l!=k: print "your set is not a group"

As you can see, I don't have experience in programming, but considering I 
started learning about a month ago, my program is not that awful.  Now I 
want to figure out how to check for identity on a set.  By identity I mean, 
given a set, there is an element in the set(let's call it e) such that for 
all elements x, x*e= e*x =x.  For example, let's say I have the set 
{e,a,b,ab}, which is accompanied by the following table:

>e*e=e        a*e=a         b*e=b              ab*e=ab
>e*a=a        a*a=e         b*a=ab             ab*a=b
>e*b=b        a*b=ab        b*b=e              ab*b=a
>e*ab=ab      a*ab=b        b*ab=a             ab*ab=e

As you might see, the set {e,a,b,ab} has an identity element, which is e. If 
you check, e*a=a and a*e=a, so e is the identity element of the set. As you 
can see, you have to do this for every element within the set.  What I need 
to do is to "check whether there is an item in the set, where (item, 
whatever)== whatever, for each whatever in the set, and also check whether 
(whatever, item) == whatever."  (I'm quoting from one of you guys, I believe 
it is from Ms. King).  Does anyone have any suggestions?

Julieta
>

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