In this paper, we tackle the following problem: compute the gcd for several univariate
polynomials with parametric coefficients. It amounts to partitioning the parameter space …

Subresultant of two univariate polynomials is a fundamental object in computational algebra
and geometry with many applications (for instance, parametric GCD and parametric …

The theory of symmetric multivariate Lagrange interpolation is a beautiful but rather
unknown tool that has many applications. Here we derive from it an Exchange Lemma that …

We consider the problem of finding a condition for a univariate polynomial having a given
multiplicity structure when the number of distinct roots is given. It is well known that such …

We present a solution for the classical univariate rational interpolation problem by means of
(univariate) subresultants. In the case of Cauchy interpolation (interpolation without …

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x−
α) m and (x− β) n with respect to the set of Bernstein polynomials {(x− α) j (x− β) d− j, 0≤ j≤ …

Subresultants of two univariate polynomials are one of the most classic and ubiquitous
objects in computational algebra and algebraic geometry. In 1948, Habicht discovered and …

We extend our previous work on Poisson-like formulas for subresultants in roots to the case
of polynomials with multiple roots in both the univariate and multivariate case, and also …

In 1853 Sylvester introduced a family of double-sum expressions for two finite sets of
indeterminates and showed that some members of the family are essentially the polynomial …

Sylvester double sums, introduced first by Sylvester (see Sylvester (1840, 1853)), are
symmetric expressions of the roots of two polynomials, while subresultants are defined …