enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Symmetric polynomial - Wikipedia

    en.wikipedia.org/wiki/Symmetric_polynomial

    Symmetric polynomials also form an interesting structure by themselves, independently of any relation to the roots of a polynomial. In this context other collections of specific symmetric polynomials, such as complete homogeneous, power sum, and Schur polynomials play important roles alongside the

  3. Power sum symmetric polynomial - Wikipedia

    en.wikipedia.org/wiki/Power_sum_symmetric_polynomial

    The following lists the power sum symmetric polynomials of positive degrees up to n for the first three positive values of . In every case, = is one of the polynomials. The list goes up to degree n because the power sum symmetric polynomials of degrees 1 to n are basic in the sense of the theorem stated below.

  4. Symmetry in mathematics - Wikipedia

    en.wikipedia.org/wiki/Symmetry_in_mathematics

    Symmetric polynomials arise naturally in the study of the relation between the roots of a polynomial in one variable and its coefficients, since the coefficients can be given by polynomial expressions in the roots, and all roots play a similar role in this setting. From this point of view, the elementary symmetric polynomials are the most ...

  5. Elementary symmetric polynomial - Wikipedia

    en.wikipedia.org/.../Elementary_symmetric_polynomial

    In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed as a polynomial in elementary symmetric polynomials.

  6. Newton's identities - Wikipedia

    en.wikipedia.org/wiki/Newton's_identities

    The Newton identities also permit expressing the elementary symmetric polynomials in terms of the power sum symmetric polynomials, showing that any symmetric polynomial can also be expressed in the power sums. In fact the first n power sums also form an algebraic basis for the space of symmetric polynomials.

  7. Symmetric algebra - Wikipedia

    en.wikipedia.org/wiki/Symmetric_algebra

    The symmetric algebra S(V) can also be built from polynomial rings.. If V is a K-vector space or a free K-module, with a basis B, let K[B] be the polynomial ring that has the elements of B as indeterminates.

  8. Complete homogeneous symmetric polynomial - Wikipedia

    en.wikipedia.org/wiki/Complete_homogeneous...

    In mathematics, specifically in algebraic combinatorics and commutative algebra, the complete homogeneous symmetric polynomials are a specific kind of symmetric polynomials. Every symmetric polynomial can be expressed as a polynomial expression in complete homogeneous symmetric polynomials.

  9. Symmetric function - Wikipedia

    en.wikipedia.org/wiki/Symmetric_function

    Aside from polynomial functions, tensors that act as functions of several vectors can be symmetric, and in fact the space of symmetric -tensors on a vector space is isomorphic to the space of homogeneous polynomials of degree on . Symmetric functions should not be confused with even and odd functions, which have a different sort of symmetry.