Looking for computer algebra systems for functional analysis

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I'm looking for a CAS that is compatible with ideas from functional analysis. Specifically I want to work with Banach algebras of functions on finite groups or semigroups, so ideally there would also be tools for working with group representation theory. I've largely used GAP until now, but the inability to easily define a function algebra on a group has been a very limiting factor so I was just wondering if there's any better tools out there.