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I think you might want to try

sage: polylog?
sage: psi?

as a first step. Does mpmath have some of what you are looking for? I'm also not sure if you are calculating more than one polylog, or a different function called a multiple polylogarithm.

I think you might want to try

sage: polylog?
sage: psi?

as a first step. Does mpmath have some of what you are looking for? I'm also not sure if you are calculating more than one polylog, or a different function called a multiple polylogarithm.But I don't see immediate Sage access to Ginac's

Li(m, x)    classical polylogarithm as well as multiple polylogarithm 
G(a, y) multiple polylogarithm 
G(a, s, y)  multiple polylogarithm with explicit signs for the imaginary parts

other than the regular polylog. However, Pynac's code doesn't seem to be missing too much of Ginac's stuff; some things are commented out, but not much.

Here is where ask.sagemath.org is NOT so helpful - no guarantee that the person who would know this best is reading. I'll ping him and see if he might give a sense of how you could write a wrapper (there are lots of good examples in Sage itself); presumably you could also access it via the C interface.

Incidentally, mpmath does not appear to currently support multiple polylogs.