ABSTRACT
The essence of error-checking is to use some simple feature of the problem to predict some simple feature of the answer—and then seeing if your answer has that simple feature. This also obviously holds for the exponentials and square roots already mentioned. In particular, square roots of polynomials don't just go away. In the same vein, certain things can occur in an answer only if they already were part of the problem: trigonometric functions do not spontaneously generate, nor do the denominators of fractions. This also obviously holds for the exponentials and square roots already mentioned. Exponentials are also forever. You can’t differentiate them away, nor integrate them away. Only logarithms can kill exponentials.
