23 citations · 92 across the 39 of their papers we have counts for
21 papers · 1 filter
Subresultants and the Shape Lemma
David A. Cox, Carlos D'Andrea
In nice cases, a zero-dimensional complete intersection ideal over a field of characteristic zero has a Shape Lemma. There are also cases where the ideal is generated by the result…
Bounds for degrees of syzygies of polynomials defining a grade two ideal
Teresa Cortadellas Benitez, Carlos D'Andrea, Eulalia Montoro
We make explicit the exponential bound on the degrees of the polynomials appearing in the Effective Quillen-Suslin Theorem, and apply it jointly with the Hilbert-Burch Theorem to s…
The Canny-Emiris conjecture for the sparse resultant
Carlos D'Andrea, Gabriela Jeronimo, Martin Sombra
We present a product formula for the initial parts of the sparse resultant associated to an arbitrary family of supports, generalising a previous result by Sturmfels. This allows t…
The Rees Algebra of Parametric Curves via liftings
Teresa Cortadellas Benitez, David Cox, Carlos D'Andrea
We study the defining equations of the Rees algebra of ideals arising from curve parametrizations in the plane and in rational normal scrolls, inspired by the work of Madsen and Ku…
Minimal solutions of the rational interpolation problem
Teresa Cortadellas Benitez, Carlos D'Andrea, Eulalia Montoro
We explore connections between the approach of solving the rational interpolation problem via resolutions of ideals and syzygies with the standard method provided by the Extended E…
Closed formula for univariate subresultants in multiple roots
Carlos D'Andrea, Teresa Krick, Agnes Szanto +1
We generalize Sylvester single sums to multisets (sets with repeated elements), and show that these sums compute subresultants of two univariate polyomials as a function of their r…
On the resolution of fan algebras of principal ideals over a Noetherian ring
Teresa Cortadellas Benitez, Carlos D'Andrea, Florian Enescu
We construct explicitly a resolution of a fan algebra of principal ideals over a Noetherian ring for the case when the fan is a proper rational cone in the plane. Under some mild c…
Subresultants in multiple roots: an extremal case
Alin Bostan, Carlos D'Andrea, Teresa Krick +2
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…
The Rees Algebra of a monomial plane parametrization
Teresa Cortadellas Benitez, Carlos D'Andrea
We compute a minimal bigraded resolution of the Rees Algebra associated to a proper rational parametrization of a monomial plane curve. We describe explicitly both the bigraded Bet…
Moving curve ideals of rational plane parametrizations
Carlos D'Andrea
In the nineties, several methods for dealing in a more efficient way with the implicitization of rational parametrizations were explored in the Computer Aided Geometric Design Comm…
Minimal generators of the defining ideal of the Rees Algebra associated to a rational plane parameterization with μ=2
Teresa Cortadellas Benitez, Carlos D'Andrea
We exhibit a set of minimal generators of the defining ideal of the Rees Algebra associated to the ideal of three bivariate homogeneous polynomials parametrizing a proper rational…
Subresultants, Sylvester sums and the rational interpolation problem
Carlos D'Andrea, Teresa Krick, Agnes Szanto
We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without…
Subresultants in Multiple Roots
Carlos D'Andrea, Teresa Krick, Agnes Szanto
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 als…
Singular factors of rational plane curves
Laurent Buse, Carlos D'Andrea
We give a complete factorization of the invariant factors of resultant matrices built from birational parameterizations of rational plane curves in terms of the singular points of…
Minimal generators of the defining ideal of the Rees Algebra associated to monoid parametrizations
Teresa Cortadellas Benitez, Carlos D'Andrea
We describe a minimal set of generators of the defining ideal of the Rees Algebra associated to a proper parametrization of any monoid hypersurface. In the case of plane curves, we…
Tropicalization and irreducibility of Generalized Vandermonde Determinants
Carlos D'Andrea, Luis Felipe Tabera
We find geometric and arithmetic conditions in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix over the algebraic closure of any field…
Sylvester's Double Sums: the general case
Carlos D'Andrea, Hoon Hong, Teresa Krick +1
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 subr…
Rational Formulas for Traces in zero-dimensional Algebras
Carlos D'Andrea, Gabriela Jeronimo
We present a rational expression for the trace of the multiplication map M_r in a finite-dimensional algebra of the form A:=K[x_1,...,x_n]/I in terms of the generalized Chow form o…
A matrix-based approach to properness and inversion problems for rational surfaces
Carlos D'Andrea, Laurent Buse
We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exi…
The Cayley-Menger determinant is irreducible for
Carlos D'Andrea, Martin Sombra
We prove that the Cayley-Menger determinant of an -dimensional simplex is an absolutely irreducible polynomial for We also study the irreducibility of polynomials asso…
On the irreducibility of the determinant of the matrix of moving planes
Carlos D'Andrea
We show that, for generic bihomogeneous polynomials, the determinant of the matrix of moving planes is irreducible.