In many respects the problem of computing the greatest common divisor of two polyno- mials is a fundamental concern of algebraic manipulation. Once pioneer computer algebra systems (such as ALPAK or PM) had routines for polynomial operations, the natural pro gression was to develop routines for the manipulation of rational functions. It soon became apparent that rational manipulation leads to a severe problem of intermediate expression swell. For example, consider the problem of adding two rational functions.
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