The polynomial invariants of the "G"-action on "V" are those polynomial functions "f" on "V" which are fixed under the 'change of variables' due to the action of the group, so that "g"·"f" = "f" for all "g" in "G". They form a commutative algebra "A" = "R"("V")"G", and this algebra is interpreted as the algebra of functions on the 'invariant theory quotient' "V" //"G" because any one of these functions gives the same value for all points that are equivalent (that is, formula_2 for all ). In the language of modern algebraic geometry,