Category: Mathematical Background

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, …

Field

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.

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

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