If "f" and "g" are polynomials in "F"["x"] for some finitely generated field "F", the Euclidean Algorithm is the most natural way to compute their GCD. However, modern computer algebra systems only use it if "F" is finite because of a phenomenon called intermediate expression swell. Although degrees keep decreasing during the Euclidean algorithm, if "F" is not finite then the bit size of the polynomials can increase (sometimes dramatically) during the computations because repeated arithmetic operations in "F" tends to lead to larger expressions. For example, the addition of two rational numbers whose denominators are bounded by "b" leads to a rational number whose denominator is bounded by "b"2, so in the worst case, the bit size could nearly double with just one operation.