It would be nice to have a command line tool with ATAT which takes as input:
-l (lattice file)
-z (tolerance for finding symmetries)
-s1 (structure 1)
-s2 (structure 2)
and then outputs whether the structures are symmetrically equivalent.
The algorithm to perform this comparison is already implemented, and used, in ATAT (e.g. by maps) so this would be a really simple programming task essentially just moving code around (but still requires some time to do).
in atat/src/
it’s not yet a very polished and/or documented code…
The problem with writing such a code is how much generality to allow for (rotation? shear? scale? displacements? supercells?)
Some feature of the corrdump code may also give you what you want.
But as a start, I have found it useful to have a tool just considering space group operations (basically what maps already does if started in a folder of two structures equivalent to each other).
But thank you for the suggestion, I will look into that.