# primitive polynomial

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**Primitive polynomial**— In field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite extension field GF( p m ). In other words, a polynomial F(X) with coefficients in GF( p ) = Z/ p Z is a primitive… … Wikipedia**primitive polynomial**— Math. a polynomial that has content equal to 1. Cf. content1 (def. 10) … Useful english dictionary**Primitive**— is a subjective label used to imply that one thing is less sophisticated or less advanced than some other thing. Being a comparative word it is also relative in nature.Indigenous peoples and their beliefs and practices are sometimes described as… … Wikipedia**Polynomial factorization**— In mathematics and computer algebra, polynomial factorization typically refers to factoring a polynomial into irreducible polynomials over a given field. Formulation of the questionOther factorizations, such as square free factorization exist,… … Wikipedia**Primitive element (finite field)**— In field theory, a branch of mathematics, a primitive element of a finite field GF ( q ) is a generator of the multiplicative group of the field, which is necessarily cyclic. The minimal polynomial of a primitive element is a primitive polynomial … Wikipedia**Polynomial basis**— In mathematics, the polynomial basis is a basis for finite extensions of finite fields.Let α ∈ GF( p m ) be the root of a primitive polynomial of degree m over GF( p ). The polynomial basis of GF( p m ) is then:{ 0, 1, alpha, ldots, alpha^{m… … Wikipedia**Polynomial**— In mathematics, a polynomial (from Greek poly, many and medieval Latin binomium, binomial [1] [2] [3], the word has been introduced, in Latin, by Franciscus Vieta[4]) is an expression of finite length constructed from variables (also known as… … Wikipedia**Primitive ring**— In mathematics, especially in the area of abstract algebra known as ring theory, the concept of left primitive ring generalizes that of matrix algebra. Every matrix ring is the endomorphism ring of a finite dimensional vector space, but a… … Wikipedia**Primitive element theorem**— In mathematics, more specifically in field theory, the primitive element theorem provides a characterization of the finite field extensions which are simple and thus can be generated by the adjunction of a single primitive element. Primitive… … Wikipedia**Polynomial ring**— In mathematics, especially in the field of abstract algebra, a polynomial ring is a ring formed from the set of polynomials in one or more variables with coefficients in another ring. Polynomial rings have influenced much of mathematics, from the … Wikipedia