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Invariant polynomial
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Invariant polynomial : ウィキペディア英語版
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
:P(\gamma x) = P(x)
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.
==References==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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