A new method for eliminating variables from polynomial equations is proposed, analyzed, evaluated and applied. Problems from many applications involve computation of resultants { polynomials obtained after eliminating variables from polynomials. Therefore e ective elimination procedures require e cient methods to compute resultants, especially those exploiting sparsity which typically exists in...

Statistical models for genetic linkage analysis of k locus diseases are k-dimensional subvarieties of a (3 − 1)-dimensional probability simplex. We determine the algebraic invariants of these models with general characteristics for k = 1, in particular we recover, and generalize, the Hardy-Weinberg curve. For k = 2, the algebraic invariants are presented as determinants of 32 × 32-matrices of l...

We address the problem of the stability of the computations of resultants and subresultants of polynomials defined over complete discrete valuation rings (e.g. Zp or k[[t]] where k is a field). We prove that Euclide-like algorithms are highly unstable on average and we explain, in many cases, how one can stabilize them without sacrifying the complexity. On the way, we completely determine the d...

This chapter is an expanded version of the lecture notes prepared by the second-named author for her introductory course at the CIMPA Graduate School on Systems of Polynomial Equations held in Buenos Aires, Argentina, in July 2003. We present an elementary introduction to residues and resultants and outline some of their multivariate generalizations. Throughout we emphasize the application of t...

In this paper, we derived recurrence relations for joint moment generating functions of nonadjacent generalized order statistics (GOS) of random samples drawn from doubly truncated class of continuous distributions. Recurrence relations for joint moments of nonadjacent GOS (ordinary order statistics (OOS) and k-upper records (k-RVs) as special cases) are obtained. Single and product moment gene...

In this paper, we investigate the computation of the moments of the compound Poisson sums with discounted claims when introducing dependence between the interclaim time and the subsequent claim size. The dependence structure between the two random variables is defined by a Farlie-Gumbel-Morgenstern copula. Assuming that the claim distribution has finite moments, we give expressions for the firs...

A relatively new branch of computational biology and chemistry has been emerging as an e ort to apply successful paradigms and algorithms from geometry and robot kinematics to predicting the structure of molecules, embedding them in Euclidean space, and nding the energetically favorable con gurations. We illustrate several e cient algebraic algorithms for enumerating all possible conformations ...