Abstract
The classical Routh's algorithm has the drawback that it involves divisions. Hence if one starts for example with integer or polynomial entries one ends up with rational numbers or rational functions respectively. Using Hurwitz determinants instead one can avoid this drawback in principle. However an efficient way to compute these determinants without introducing fractions has been missing. An algorithm to compute these determinants in a fraction free manner is presented. It is shown that this algorithm is optimal with respect to the growth of the entries.
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