evaluate a polynomial approximation to the function:
To consider a trivial example, if T*T isn't a T, then one can't evenresult = A + B* T + C * T^2 + D * T^3...
to give a concrete example, the root finding algorithm that started this
thread uses a polynomial approximation to the function to greatly speed up
finding the root (we can find the polynomial approximation and it's root
algebraically once we have evaluated enough points in the function). It's
this insight that makes the algorithm converge so rapidly compared to the
alternatives, but requiring that T*T != T breaks the underlying assumptions
not only in how it's implemented, but in how it actually works
algorithmically.