algebraic normal form

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algebraic normal form

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"Algebraic" would refer to the fact that a two-element Galois field, ${\displaystyle \mathbb {F} _{2}}$ adjoined with some variables forms a polynomial algebra, ${\displaystyle \mathbb {F} _{2}[x_{1},...,x_{n}]}$.

algebraic normal form (uncountable)

1. (algebra, logic) ring sum normal form
   • 2015 September 22, Magnus Gausdal Find, Joan Boyar, “Multiplicative Complexity of Vector Valued Boolean Functions”, in arxiv.org‎^[1], retrieved 2017-08-10:

         It is well known that every ${\displaystyle (n,1)}$-function ${\displaystyle f}$ can be written uniquely as a multilinear polynomial over ${\displaystyle \mathbb {F} _{2}}$
     ${\displaystyle \qquad \qquad \qquad \qquad \qquad f(x_{1},...,x_{n})=\sum _{X\subseteq [n]}\alpha _{X}\prod _{i\in X}x_{i}}$.
     This polynomial is called the Zhegalkin polynomial or the algebraic normal form (ANF) of ${\displaystyle f}$.

• ring sum normal form

• Zhegalkin polynomial