Computer algebra is that part of computer science which designs, analyzes, implements, and applies algebraic algorithms. (Buchberger, Loos)

While it is arguable whether computer algebra is part of computer
science or mathematics, we certainly agree with the rest of the
statement.
In fact, in our view computer algebra is a special form of
scientific computation, and it comprises a wide range of basic goals,
methods, and applications. In contrast to numerical computation the
emphasis is on computing with symbols representing mathematical
concepts. Of course that does not mean that computer algebra is devoid
of computations with numbers. Decimal or other positional
representations of integers, rational numbers and the like appear in
any symbolic computation. But integers or real numbers are not the
sole objects. In addition to these basic numerical entities computer
algebra deals with polynomials, rational functions, trigonometric
functions, algebraic numbers, etc. That does not mean that we will not
need numerical algorithms any more. Both forms of scientific
computation have their merits and they should be combined in a
computational environment. For instance, in order to compute an
approximate solution to a differential equation it might be reasonable
to determine the first *n* terms of a power series solution by exact
methods from computer algebra before handing these terms over to a
numerical package for evaluating the power series.