ABSTRACT
This chapter is concerned with the applicability and correctness of various mathematical transformations. It examines potential sources of error in computer algebra systems as well as practical and theoretical limitations on their use. The chapter discusses three sources of spurious solutions: extraneous roots of equations, improper integrals, and antiderivatives having singularities that do not match those of the integrand. Trigonometric equations occur frequently in college mathematics, as well as scientific and engineering applications. While computer algebra systems provide impressive computational capabilities, they are far from being a universal panacea for mathematical problem solving. The treatment of indeterminate forms presents a major difficulty for computer algebra systems. An important capability of a computer algebra system is its ability to solve equations symbolically. Computer algebra systems are extraordinarily powerful mathematical assistants. When tackling mathematical problems, both humans and computer algebra systems sometimes use procedures that introduce spurious solutions.
