polynomial basis

Fetched 2026-10-26 (cache).

Datamuse reports no synonyms or antonyms for this word.

Noun

1. {{lb|en|algebra|ring theory}} A [[basis]] of a [[polynomial ring]] (said ring being viewed either as a [[vector space]] over the [[field]] of coefficients or as a [[free module]] over the [[ring]] of coefficients).
2. {{lb|en|algebra|field theory|cryptography|of a finite field}} ''Specifically'', a basis, of the form <big>{</big>1, ''α'', ..., ''α''^''n''-1<big>}</big>, of a finite [[extension field|extension]] '''F'''_''qⁿ'' of a [[Galois field]] '''F'''_''q'', where ''α'' is a [[primitive element]] of '''F'''_''qⁿ'' (i.e., a [[root]] of a degree-''n'' [[primitive polynomial]] over '''F'''_''q'').

Source: Wiktionary · CC BY-SA 4.0 (Wiktionary dump) · cached copy, not a rewrite.