geom::LinearTransform and geom::AffineTransform both use invert to return an inverted copy of the transform, which sounds like it modifies the transform in place. afw Transform and astshim Mapping use getInverted to return an inverted copy of the transform, which is clearer but a bit verbose.
I would like to standardize all of these to inverted, which is clear and concise and matches other modern usage in our code, e.g. sphgeom.
I would also like to rename simplify to simplified in astshim for clarity and consistency (this is not widely used and would be a very small change).
The changes proposed would require small changes to roughly a dozen packages. I'm happy to do the work. If folks want less churn then a smaller scale version of the proposal is to switch inverse to getInverted (and simplify to getSimplified, for consistency).