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Use polynomial rings, I suspect. If there is in fact such functionality with Groebner bases etc. - you are closer to that environment than I am nowadays.

I tried using eqs[0].roots(ring=RR) and the like, but this gave a nasty error.

As for the Maxima, the point is exact solutions, so this is what to expect. There is something called [algsys]( in Maxima that should be refinable to your needs, though Maxima does this rational substitution thing a lot, even when we ask it not to.