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词汇 Invariant polynomial
分类 英语词汇 英语翻译词典
释义

Invariant polynomial

英语百科

Invariant polynomial

In mathematics, an invariant polynomial is a polynomial P that is invariant under a group \Gamma acting on a vector space V. Therefore P is a \Gamma-invariant polynomial if

for all \gamma \in \Gamma and x \in V.

Cases of particular importance are for Γ a finite group (in the theory of Molien series, in particular), a compact group, a Lie group or algebraic group. For a basis-independent definition of 'polynomial' nothing is lost by referring to the symmetric powers of the given linear representation of Γ.

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