Symmetrica allows nearly all computations inside the algebra of symmetric functions. You can easily change basis between the different bases of the algebra of symmetric functions.
There are also many routines to switch from the symmetric function to
the symmetric polynomial via specifying the length of the alphabet.
Also generalisations of the symmetric polynomials/functions are available.
In Symmetrica for example we have the following routines:
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symmetrica (at) symmetrica.de