Cryptography - Sage

sage: n = 12sage: for i in range(n):....: if gcd(i,n) == 1:....: print i # now hit enter twice....:15711Putting together our use of sets, we demonstrate the use of if and while loops to constructthe same set of integers in 0,..,n:sage: n = 12sage: r = euler_phi(n)sage: i = 1sage: S = set([i])sage: while len(S) < r:....: i += 1....: if GCD(i,n) == 1:....: S.add(i) # hit enter twice....:sage: Sset([1, 11, 5, 7])In each instance the indentation level is crucial to determine the limits of the loops, whichcan consist of several lines of commands.Python StringsA useful Python types for this course will be strings, which can be created by enclosinginput in double quotes or in single quotes.94 Appendix A. SAGE Constructions