Is Perm a Basic object? If so, you should get acquainted with the
requirements about obj.func(*obj.args)==obj. Is it tested in
test_args.py? If it is not a Basic object, why not?

I am asking all this, because it may interfere with your decision to
use some parameters in the constructor.

You should also ensure that you have consistent hash values?

Does the following work

>>> a = Perm(some_arguments)
>>> b = Perm(the_same_arguments)
>>> a == b
True I presume
>>> hash(a) == hash(b)
True I hope
>>> id(a) == id(b)
False most probably, unless caching works really well

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