  We prove a factorization formula for the Taylor series coefficients of a zero
of a polynomial as a function of the polynomial's coefficients. This result
extends to more general functions which we call "complex-exponent polynomials".
To prove this formula, we prove theorems about derivations on commutative
rings. We also show that, when applied to polynomials, our formula recovers the
results of Sturmfels obtained with GKZ systems ("Solving algebraic equations in
terms of $\mathcal{A}$-hypergeometric series". Discrete Math. 210 (2000) pp.
171-181)
