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- Symmetric_polynomial abstract "In mathematics, a symmetric polynomial is a polynomial P(X1, X2, …, Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally, P is a symmetric polynomial, if for any permutation σ of the subscripts 1, 2, ..., n one has P(Xσ(1), Xσ(2), …, Xσ(n)) = P(X1, X2, …, Xn).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 fundamental symmetric polynomials. A theorem states that any symmetric polynomial can be expressed in terms of elementary symmetric polynomials, which implies that every symmetric polynomial expression in the roots of a monic polynomial can alternatively be given as a polynomial expression in the coefficients of the 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 elementary ones. The resulting structures, and in particular the ring of symmetric functions, are of great importance in combinatorics and in representation theory.".
- Symmetric_polynomial wikiPageID "1440207".
- Symmetric_polynomial wikiPageRevisionID "604794178".
- Symmetric_polynomial hasPhotoCollection Symmetric_polynomial.
- Symmetric_polynomial subject Category:Polynomials.
- Symmetric_polynomial subject Category:Symmetric_functions.
- Symmetric_polynomial type Abstraction100002137.
- Symmetric_polynomial type Function113783816.
- Symmetric_polynomial type MathematicalRelation113783581.
- Symmetric_polynomial type Polynomial105861855.
- Symmetric_polynomial type Polynomials.
- Symmetric_polynomial type Relation100031921.
- Symmetric_polynomial type SymmetricFunctions.
- Symmetric_polynomial comment "In mathematics, a symmetric polynomial is a polynomial P(X1, X2, …, Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial.".
- Symmetric_polynomial label "Polinomio simmetrico".
- Symmetric_polynomial label "Polinomio simétrico".
- Symmetric_polynomial label "Polynôme symétrique".
- Symmetric_polynomial label "Symmetric polynomial".
- Symmetric_polynomial label "Symmetrisches Polynom".
- Symmetric_polynomial label "Wielomian symetryczny".
- Symmetric_polynomial label "Симметрический многочлен".
- Symmetric_polynomial label "対称式".
- Symmetric_polynomial label "對稱多項式".
- Symmetric_polynomial sameAs Symmetrisches_Polynom.
- Symmetric_polynomial sameAs Συμμετρικό_πολυώνυμο.
- Symmetric_polynomial sameAs Polinomio_simétrico.
- Symmetric_polynomial sameAs Polynôme_symétrique.
- Symmetric_polynomial sameAs Polinomio_simmetrico.
- Symmetric_polynomial sameAs 対称式.
- Symmetric_polynomial sameAs Wielomian_symetryczny.
- Symmetric_polynomial sameAs m.051rlw.
- Symmetric_polynomial sameAs Q930499.
- Symmetric_polynomial sameAs Q930499.
- Symmetric_polynomial sameAs Symmetric_polynomial.
- Symmetric_polynomial wasDerivedFrom Symmetric_polynomial?oldid=604794178.
- Symmetric_polynomial isPrimaryTopicOf Symmetric_polynomial.