From Mathematics to Generic Programming

13. A Real-World Application

I am fairly familiar with all forms of secret writings, and am myself the author of a trifling monograph upon the subject, in which I analyze one hundred and sixty separate ciphers, but I confess that this is entirely new to me.

Sherlock Holmes

Throughout this book, we’ve seen examples of important algorithms that came out of work on number theory. We’ve also seen how attempts to generalize those mathematical results brought about the development of abstract algebra, and how its ideas about abstraction led directly to the principles of generic programming. Now we’re going put it all together. We’ll show how our mathematical results and our generalized algorithms can be used to implement a real-world application: a ...