primitive element

短语

[计] 原始元素

词形变化

primitive elements 复数 primitive elements

释义与例句

n.
  1. 1.

    An element that generates a simple extension.

    数学
  2. 2.

    An element that generates the multiplicative group of a given Galois field (finite field).

    数学

    Furthermore, if the irreducible polynomial has a primitive element α (where α=1) that is a root, then the polynomial is termed a primitive polynomial and corresponds to the polynomial for a maximal length feedback shift register.

    2003, Soonhak Kwon, Chang Hoon Kim, Chun Pyu Hong, Efficient Exponentiation for a Class of Finite Fields GF(2ⁿ) Determined by Gauss Periods, Colin D. Walter, Çetin K. Koç, Christof Paar (editors), Cryptographic Hardware and Embedded Systems, CHES 2003: 5th International Workshop, Proceedings, Springer, LNCS 2779, page 228, Also in the case of a Gauss period of type (n,1), i.e. a type I optimal normal element, we find a primitive element in GF(2ⁿ) which is a sparse polynomial of a type I optimal normal element and we propose a fast exponentiation algorithm which is applicable for both software and hardware purposes.

    Here, necessarily, c must be a primitive element of 𝔽_𝕢, since this is the norm of a root of the polynomial.

  3. 3.

    Given a modulus n, a number g such that every number coprime to n is congruent (modulo n) to some power of g; equivalently, a generator of the multiplicative field of integers modulo n.

    数学
  4. 4.

    An element that is not a positive integer multiple of another element of the lattice.

    数学
  5. 5.

    An element x ∈ C such that μ(x) = x ⊗ g + g ⊗ x, where μ is the comultiplication and g is an element that maps to the multiplicative identity 1 of the base field under the counit (in particular, if C is a bialgebra, g = 1).

    数学

    2009, Masoud Khalkhali, Basic Noncommutative Geometry, European Mathematical Society, page 29, A primitive element of a Hopf algebra is an element h∈H such that Δh=1⊗h+h⊗1. It is easily seen that the bracket [x,y]:=xy-yx of two primitive elements is again a primitive element. It follows that primitive elements form a Lie algebra. For H=U(g) any element of g is primitive and in fact using the Poincaré-Birkhoff-Win theorem, one can show that the set of primitive elements of U(g) coincides with the Lie algebra g.

  6. 6.

    An element of a free generating set of a given free group.

    数学