irreducible polynomial

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• Irreducible polynomial — In mathematics, the adjective irreducible means that an object cannot be expressed as a product of at least two non trivial factors in a given set. See also factorization. For any field F , the ring of polynomials with coefficients in F is… …   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

• 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

• Irreducible (mathematics) — In mathematics, the term irreducible is used in several ways. * In abstract algebra, irreducible can be an abbreviation for irreducible element; for example an irreducible polynomial. * In representation theory, an irreducible representation is a …   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

• irreducible — irreducibility, irreducibleness, n. irreducibly, adv. /ir i dooh seuh beuhl, dyooh /, adj. 1. not reducible; incapable of being reduced or of being diminished or simplified further: the irreducible minimum. 2. incapable of being brought into a… …   Universalium

• irreducible — 1. adjective /ˌɪrɪˈdjuːsɪbəl/ a) Not able to be reduced or lessened. b) Not able to be brought to a simpler or reduced form. Ant: reducible 2. noun /ˌɪrɪˈdjuːsɪbəl/ …   Wiktionary

• irreducible function — noun : an integral rational function of a polynomial that cannot be resolved into integral rational factors of lower degree with coefficients in the same number field …   Useful english dictionary

• Separable polynomial — In mathematics, two slightly different notions of separable polynomial are used, by different authors. According to the most common one, a polynomial P(X) over a given field K is separable if all its roots are distinct in an algebraic closure of… …   Wikipedia

• 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