We show a method for constructing a polynomial interpolating roots' multiplicities of another polynomial, that does not use companion matrices. This leads to a modification to Guersenzvaig– Szechtman square-free decomposition algorithm that is more efficient both in theory and in practice. The problem of computing the square-free decomposition of a… (More)
We show that a linear-time algorithm for computing Hong's bound for positive roots of a univariate polynomial, described by K. Mehlhorn and S. Ray in an article " Faster algorithms for computing Hong's bound on absolute positiveness " , is incorrect. We present a corrected version.
We present algorithms for square classes, quadratic forms and Witt classes of quadratic forms over the eld of rational functions of one variable over the reals. The algorithms are capable of: nding the unique representative of a square class, deciding if a given function is a square or a sum of squares and deciding if a quadratic form is isotropic or… (More)