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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. That is, any symmetric polynomial P is given by an expression involving only additions…

Products, Properties & Fundamental theorem of symmetric polynomials

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Properties

19 related topics

Fundamental theorem of symmetric polynomials

12 related topics

Definition

2 related topics

Recursive definition

1 related topics

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Definition

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Properties

Fundamental theorem of symmetric polynomials

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Elementary symmetric polynomial

Nodes45
Edges44
Triples29
Avg. degree1.96
Density0.044444
Components1

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Elementary symmetric polynomial

Top relations

related to Alternative proof · 10
Elementary symmetric polynomial → Assume, Furthermore, Lemma, Order, The, X1, X2, Xi, Xn, Young
related to Properties · 7
Elementary symmetric polynomial → That, The, These, Vieta's, X1, X2, Xn
related to Definition · 5
Elementary symmetric polynomial → Also, In, The, X1, Xn
related to Fundamental theorem of symmetric polynomials · 5
Elementary symmetric polynomial → For, Sn, This, X1, Xn
related to Examples · 2
Elementary symmetric polynomial → For, The

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Important terminology

symmetric polynomial polynomials x1 xn elementary variables one degree homogeneous sum ring monomial coefficients monomials displaystyle lacunary products also proof

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SubjectPredicateObjectConfidenceSrc
Elementary symmetric polynomialrelated to Alternative proofThe0.60section
Elementary symmetric polynomialrelated to Alternative proofX10.60section
Elementary symmetric polynomialrelated to Alternative proofXn0.60section
Elementary symmetric polynomialrelated to Alternative proofAssume0.60section
Elementary symmetric polynomialrelated to Alternative proofOrder0.60section
Elementary symmetric polynomialrelated to Alternative proofXi0.60section
Elementary symmetric polynomialrelated to Alternative proofX20.60section
Elementary symmetric polynomialrelated to Alternative proofFurthermore0.60section
Elementary symmetric polynomialrelated to Alternative proofYoung0.60section
Elementary symmetric polynomialrelated to Alternative proofLemma0.60section
Elementary symmetric polynomialrelated to DefinitionThe0.60section
Elementary symmetric polynomialrelated to DefinitionX10.60section

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