[Tutor] tables and dictionaries

[Tim Peters]

[Julieta Rangel]
> I'm trying to write a program that given a finite set (say, up to 30
> elements) and a table, the program figures out whether the set is a
> group.  I need to have the user enter the elements on the set and
> store them on a list.  Once on this list, I want the user to enter
> a table, but for this, I need for python to pair each element with
> every element on the list so I can ask for the table.

Hmm!  For a set with 30 elements, that's 30*30 == 900 "products".  So you may
want to read this information from a file instead.

> Let's say that the set consists of elements
> [e,a,b,ab].  I need to ask the user
>
> e*e=?        a*e=?         b*e=?              ab*e=?
> e*a=?        a*a=?         b*a=?              ab*a=?
> e*b=?        a*b=?         b*b=?              ab*b=?
> e*ab=?       a*ab=?        b*ab=?             ab*ab=?
>
> Since I don't know what the set will consist of, I need to find a way
> so that once the user enters the set, the computer pairs the elements
> together as I did above, asks for the required input and stores it in
> a dictionary.  Can this be done?

Yes, and quite easily (if you know how <wink>) -- I'll attach a small
program.  Here's a sample run, where to *try* to make it clearer I've
artificially added "<>" brackets around the input I typed in; everything else
is program output:

Enter comma-separated list of elements, like a,b,c: <a,b>
a*a=? <a>
a*b=? <b>
b*a=? <c>
Oops! c is not in ['a', 'b'] -- try again.
b*a=? <b>
b*b=? <a>
a * a = a
a * b = b
b * a = b
b * b = a

> If so, how?  If this can be done, it would be easier to check for
> the four properties of a group[closure under binary operation,

Note that the program above rejected my attempt to enter c, so the *input*
routine ensures closure.

> associativity : a*(a*b)=(a*a)*b; identity and inverses).
> ...

These are, of course, harder to check.  I wouldn't call it "tedious", though!
It seems like a very nice exercise for learning how to use loops and logic.

oh-ok-it's-tedious<wink>-ly y'rs  - tim

import string

elts = raw_input("Enter comma-separated list of elements, like a,b,c: ")
elts = string.split(elts, ",")

product = {}
for x in elts:
    for y in elts:
        prompt = "%s*%s=? " % (x, y)
        need_good_result = 1
        while need_good_result:
            z = raw_input(prompt)
            if z in elts:
                need_good_result = 0
            else:
                print "Oops!", z, "is not in", elts, "-- try again."
        product[x, y] = z

# Display the table.
items = product.items()
items.sort()
for (x, y), z in items:
    print x, "*", y, "=", z