= Reynolds operator on a polynomial invariant ring
{c}
{title2=$\mathcal R(f)=\int_K k\cdot f\,dk$}
= Reynolds operator
{c}
{synonym}
In characteristic zero, averaging over a compact group, or over a Zariski-dense compact form of a complex reductive group, gives a degree-preserving projection onto the <polynomial invariant ring>. Its module property is $\mathcal R(af)=a\mathcal R(f)$ for invariant $a$. This property turns finite ideal generation in the ambient polynomial ring into finite algebra generation of the invariant subring.
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