Expansion happens in the power series ring as expected(?):

sage: R.<x>=PowerSeriesRing(QQ,'x')
sage: 1/(x^2 - x - 1)
-1 + x - 2*x^2 + 3*x^3 - 5*x^4 + 8*x^5 - 13*x^6 + 21*x^7
 - 34*x^8 + 55*x^9 - 89*x^10 + 144*x^11 - 233*x^12 + 377*x^13
 - 610*x^14 + 987*x^15 - 1597*x^16 + 2584*x^17 - 4181*x^18 + 6765*x^19 + O(x
^20)

I personally would rather implement analytical functionality on top
of the power series ring but am not an expert in either.

Regards,

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