We give an algorithm for the interpolation of a polynomial A given by a straight-line program.
Its complexity is polynomial in τ, log (d), L, n, where τ is an input bound on the number of …

The fundamental theorem of symmetric polynomials states that for a symmetric polynomial f_
{Sym} in C [x_1, x_2,..., x_n], there exists a unique" witness" f in C [y_1, y_2,..., y_n] such that …

Despite the relevance of the binomial distribution for probability theory and applied statistical
inference, its higher-order moments are poorly understood. The existing formulas are either …

We study the cost of multiplication modulo triangular families of polynomials. Following
previous work by Li et al.(2007), we propose an algorithm that relies on homotopy and fast …

This paper presents some applications using several properties of three important symmetric
polynomials: elementary symmetric polynomials, complete symmetric polynomials and the …

Journal of Symbolic Computation Evaluation properties of invariant polynomials Page 1 Journal
of Symbolic Computation 44 (2009) 1592–1604 Contents lists available at ScienceDirect …

Let $\mathbb {K}[x_1,\dots, x_n] $ be a multivariate polynomial ring over a field $\mathbb {K}
$. Let $(u_1,\dots, u_n) $ be a sequence of $ n $ algebraically independent elements in …

In this thesis we study the following three topics, which share a connection through the
(arithmetic) circuit complexity of polynomials. 1. Rank of symbolic matrices. 2. Computation …

Using evaluation at appropriately chosen points, we propose a Gr\" obner basis free
approach for calculating the secondary invariants of a finite permutation group. This …

Cette thèse porte sur trois problèmes en combinatoire algébrique effective et algorithmique.
Les premières parties proposent une approche alternative aux bases de Gröbner pour le …