algebraic normal form

English

Etymology

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

Noun

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

Synonyms

• ring sum normal form

See also

• Zhegalkin polynomial