## Math, algorithms and programming languages

A few weeks ago I started reading Number Theory for Computing by Song Y. Yan (amazing book by the way!) and in the first chapter we learned about the Euclidean Algorithm, or how to find the Greatest Common Divisor, probably the oldest non trivial algorithm surviving to the present days (which, btw, probably it wasn’t “invented” by Euclid but “documented”).

What called my attention is the way we take the algorithm and model or move it into a programming language, a quick search got me this answer from StackOverflow, I will copy the second answer from that question:

def gcd(x, y):
while y != 0:
(x, y) = (y, x % y)
return x


This is very similar to the “loop” code in the previous Wikipedia article:

function gcd(a, b)
while b ≠ 0
t := b;
b := a mod b;
a := t;
return a;


Wikipedia has a recursive version as well:

function gcd(a, b)
if b = 0
return a;
else
return gcd(b, a mod b);


And the same StackOverflow question has a recursive answer too:

def gcd_recursive(a, b):
if b == 0:
return a
else:
return gcd_recursive(b, a % b)


I decided to implement the same algorithm using Elixir first to see how “clear” would it look:

defmodule Num do
def gcd(a, 0), do: a
def gcd(a, b), do: gcd(b, rem(a, b))
end


Wow, I was surprised, when you are used to it immediately your brain wire up the conditions and say “ah ok, we need this escape condition” or “we need to cover this pattern”, the version in OCaml is very similar as well:

let rec gcd a, b =
if b = 0 then a else gcd b (a mod b)
;;


Probably is just me, but I like the way we can express a lot easier math concepts in a functional programming language. (Yes, I know, I am probably late to the party).