Related papers: Explicit formulas for the multivariate resultant

We present formulas for computing the resultant of sparse polynomials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous…

The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable (the resultant is a polynomial in the…

We present an explicit formula for computing toric residues as a quotient of two determinants, a la Macaulay, where the numerator is a minor of the denominator. We also give an irreducible representation of toric residues by extending the…

In this note, we consider the resultant of systems of homogeneous multivariate polynomials which are equivariant under the action of direct product of two symmetric groups. We establish a decomposition formula for the resultant of such…

Constructive methods for matrices of multihomogeneous (or multigraded) resultants for unmixed systems have been studied by Weyman, Zelevinsky, Sturmfels, Dickenstein and Emiris. We generalize these constructions to mixed systems, whose…

In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into…

Given a system of n homogeneous polynomials in n variables which is equivariant with respect to the canonical actions of the symmetric group of n symbols on the variables and on the polynomials, it is proved that its resultant can be…

A fundamental problem in computational algebraic geometry is the computation of the resultant. A central question is when and how to compute it as the determinant of a matrix. whose elements are the coefficients of the input polynomials…

We provide, in a 474 pages study, a comprehensive and self-contained treatment of Resultant Theory for a homogeneous system of polynomials with several variables (as many variables as of polynomials). In a non classical way, we use the…

We provide conditions and algorithmic tools so as to classify and construct the smallest possible determinantal formulae for multihomogeneous resultants arising from Weyman complexes associated to line bundles in products of projective…

The classical multidimensional resultant can be defined as the, suitably normalized, generator of a projective elimination ideal in the ring of universal coefficients. This is the approach via the so-called inertia forms or…

Effective computation of resultants is a central problem in elimination theory and polynomial system solving. Commonly, we compute the resultant as a quotient of determinants of matrices and we say that there exists a determinantal formula…

In this paper, the discriminant of homogeneous polynomials is studied in two particular cases: a single homogeneous polynomial and a collection of n-1 homogeneous polynomials in n variables. In these two cases, the discriminant is defined…

In this paper, we develop two variants of Bezout subresultant formulas for several polynomials, i.e., hybrid Bezout subresultant polynomial and non-homogeneous Bezout subresultant polynomial. Rather than simply extending the variants of…

This note presents the multivariate Hermite criterion: a practical and powerful algorithm for determining the number of distinct real and complex roots of a zero-dimensional system of polynomials in any finite number of variables. The final…

I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables.

In this work we deduce explicit formulae for the elements of the matrices that represent the action of integro-differential operators over the coefficients of generalized Fourier series. Our formulae are obtained by performing operations on…

We introduce the DeterminantalRepresentations package for Macaulay2, which computes definite symmetric determinantal representations of real polynomials. We focus on quadrics and plane curves of low degree (i.e. cubics and quartics). Our…

In this paper we give a new and simple algorithm to put any multivariate polynomial into a normal determinant form in which each entry has the form , and in each column the same variable appears. We also apply the algorithm to obtain a…

Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the…