I=inverse(f,S)
If $S$ is an instance of LieIdeal, then $I$ is of type LieIdeal. If $S$ is an instance of LieSubAlgebra but not of LieIdeal, then $I$ is of type LieSubAlgebra. Otherwise, $I$ is of type LieSubSpace.
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The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/GradedLieAlgebras/doc.m2:1362:0.