A super-friendly guide to finite fields for programmers Chapter 1

Going from FizzBuzz to writing your own Finite Field Arithmetic Library

Apologies for the Paywall

LeetArxiv and the Finite Field Assembly (FF-asm) programming language are entirely funded by our Substack readers. Thank you for your understanding and support!

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Introduction

This is a pre-print of our upcoming book, Finite Fields for Programmers. It is a well-researched guide designed to help programmers grasp the mathematical theory of finite fields without requiring an advanced degree in mathematics. This is the resource I wish I had when I first learned about finite fields. We write all our code in C89, to ensure maximum readability among all programmers. Reach out if you translate all the problems to a different programming language.

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Chapter 1 : FizzBuzz, Division and the Modulo Operator

By the end of this chapter, you will understand that FizzBuzz is a problem in GF(3) and GF(5).

Definitions

1. Finite field - a mathematical system with a finite number of elements, where you can perform addition, subtraction, multiplication, and division (except by zero) while staying within the field.

2. Galois Field (GF) - another name for a finite field, named after Evariste Galois. Galois is pronounced as “Galwa”.

1.0 Fizzbuzz : A programmer’s introduction to finite field theory

1.0.1 What is FizzBuzz?

Fizzbuzz is a technical interview question designed to test basic programming knowledge. The problem is infamous among techies, as seen in the article, FizzBuzz still works.

VicVijayakumar on Twitter talks about the infamous FizzBuzz test

While seemingly simple, this problem provides an excellent foundation for exploring finite field theory.