Computing determinants of rational functions

Authors:
Yasushi Umeda;Tateaki Sasaki
Affiliations:
University of Tsukuba, Tsukuba-shi, Ibaraki, Japan;University of Tsukuba, Tsukuba-shi, Ibaraki, Japan
Venue:
ACM Communications in Computer Algebra
Year:
2006

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Abstract

Computation of determinants of rational functions seems to be out of thought in computer algebra so far. We first show that representing the rational function by the sum of partial fractions is absolutely necessary in the computation. We then propose a very simple technique for efficient computation: replace every distinct denominator of the rational functions in the input matrix by the inverse of an independent variable, and recover the denominators after computing the determinant as a polynomial. Some experiments show that the technique speeds up the computation by 3 ~ 6 times for the samples tested.