We show that the height of a toric variety with respect to a toric metrized line bundle can be
expressed as the integral over a polytope of a certain adelic family of concave functions. To …

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 …

Certain foams and relations on them are introduced to interpret functors and natural
transformations in categories of representations of iterated wreath products of cyclic groups …

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 generalize Sylvester single sums to multisets and show that these sums compute
subresultants of two univariate polynomials as a function of their roots independently of their …

We estimate the number| A _ λ|| A λ| of elements on a nonlinear family AA of monic
polynomials of F _ q TF q T of degree r having factorization pattern λ:= 1^ λ _1 2^ λ _2 ... r^ λ …

It is well known that for two univariate polynomials over the complex number field the
number of their common roots is equal to the order of their resultant. In this paper, we show …