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P.S. my project is on:

https://github.com/alessandro-bernardini/SAPICE

and it is a full work in progress. The documentation has to be adjusted and rewritten because at the moment the documentation does not (more) match "the reality" in the software class SmallSignalLinearCircuit.

The class reads a ngspice netlist (for the moment only BJT are supported as active elements) computes the small signal linear(ized) circuit and the corresponding nodal equations that can be solved symbolically or numerically (with sage).

Impedances can be computed symbolically or numerically (and the two port network parameters) ... and poles/zeros as far as the polynomial degree allows a symbolic solution ( <= 4 ).

"Automatic" simplification is thus a key concept, and only those terms have to be considered that "dominates" and the others ignored.

For this functions like symplify_rational_func will play an important role.