“elementary symmetric polynomial”的概念、定义、习题解题方法及翻译-数学辞典

单词

elementary symmetric polynomial

释义

elementary symmetric polynomial

For three variables, α, β, γ, the elementary symmetric polynomials are

These expressions generalize naturally to n variables, with σk being the sum of the $inline$ products of k of the variables. The elementary symmetric polynomials appear in Viète's formulae.

The elementary symmetric polynomials are symmetric functions, and any symmetric polynomial can be expressed in terms of the elementary symmetric polynomials. For example, if sk = α^k + β^k + γ^k, then

gives a general recursive means of expressing sk in terms of σ1,σ2,…,σk. See Newton's identities.

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