Practical tutorial on Algebraic Norm Form (ANF)
Published on 16 Feb 2024
$\newcommand\eps{\varepsilon} \newcommand\F{\mathbb{F}} \newcommand\floor[1]{\left\lfloor #1 \right\rfloor} \newcommand\pround[1]{\left( #1 \right)} \newcommand\proundd[1]{\big( #1 \big)} \newcommand\psquare[1]{\left[ #1 \right]} \newcommand\pset[1]{\left\{ #1 \right\}} \newcommand\psize[1]{\left| #1 \right|} \newcommand\pabs[1]{\left| #1 \right|} \newcommand\inprod[1]{\left\langle #1 \right\rangle}$
Introduction
Basics
* Prec-involution
Practical usage
* Computation (Mobius) * Sums to zero over spaces (higher-order differential = integral) * Compute concrete terms from prec-involution
Theoretical usage
* Minimum weight of a BF * Degree-n iff sums to 1 * Some degree bounds
In [None]: