## Table of Contents

These will be a series post about FFT and the math structure behind it. My goal are:

- Going back fundamentally to the polynomial ring and isomorphism.
- Analyse the fft implementations in Plonky3, Gnark-crypto, arkworks

However, …

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# Category: Mathematical Background

## FFT Part 1: 8 Points NTT Butterfly

## Table of Contents

## Abstract Algebra

###### Field

Learning new things!

These will be a series post about FFT and the math structure behind it. My goal are:

- Going back fundamentally to the polynomial ring and isomorphism.
- Analyse the fft implementations in Plonky3, Gnark-crypto, arkworks

However, …

In abstract algebra, a field is a set equipped with two operations, usually called addition and multiplication. These operations satisfy several properties, which we outline below.

**Closure**: For any two elements \( a \) and \( b \) in a field \( F \), the sum \( a