Factorization of polynomials over finite fields: Difference between revisions

Revision as of 09:42, 7 February 2022

Revision as of 09:42, 7 February 2022

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In [[mathematics]] and [[computer algebra]] the [[factorization of polynomials|factorization of a polynomial]] consists of decomposing it into a [[product (mathematics)|product]] of [[irreducible polynomial|irreducible factors]]. This decomposition is theoretically possible and is unique for [[polynomial]]s with [[coefficient]]s in any [[field (mathematics)|field]], but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an [[algorithm]]. In practice, algorithms have been designed only for polynomials with coefficients in a [[finite field]], in the [[field of rationals]] or in a [[finitely generated field extension]] of one of them.