Introduction to Cryptography with Open-Source Software

Introduction to Sage 405

....: f = [q for q,e in factor(p-1)]

....: print p, f[-1]

....:

3 2

5 2

7 3

11 5

13 3

17 2

19 3

23 11

29 7

The next program lists subsets:

sage: for s in subsets([1,2,3]):

....: print s

....:

[]

[1]

[2]

[1, 2]

[3]

[1, 3]

[2, 3]

[1, 2, 3]

The while loop continues looping until a particular criterion is satisfied. Here

is an example: finding the smallest power of two that contains all ten digits

(such a number is called pandigital). Start with noting that if n is any integer,

then

set([x for x in str(n)])

will pr oduce a set containing the string versions of all integers in n:

sage: n = 2^20

sage: set([x for x in str(n)])

set([’1’, ’0’, ’5’, ’4’, ’7’, ’6’, ...