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- Saugata Basu, Martín Sombra
- Discrete & Computational Geometry
- 2016

We present a polynomial partitioning theorem for finite sets of points in the real locus of a complex algebraic variety of codimension at most two. This result generalizes the polynomial partitioning… (More)

We present bounds for the degree and the height of the polynomials arising in some problems in effective algebraic geometry including the implicitization of rational maps and the effective… (More)

- Gabriela Jeronimo, Teresa Krick, Juan Sabia, Martín Sombra
- Foundations of Computational Mathematics
- 2004

We present a bounded probability algorithm for the computation of the Chow forms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the… (More)

- Martin Avendano, Teresa Krick, Martín Sombra
- J. Complexity
- 2007

We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K[x, y] over an algebraic number field K and their multiplicities, whose… (More)

The study of the Newton polytope of a parametric hypersurface is currently receiving a lot of attention both because of its computational interest and its connections with Tropical Geometry,… (More)

- Saugata Basu, Martín Sombra
- ArXiv
- 2014

We present a polynomial partitioning theorem for finite sets of points in the real locus of a complex algebraic variety. This result generalizes the polynomial partitioning theorem on the Euclidean… (More)

- Carlos D'Andrea, Martín Sombra
- Mathematics in Computer Science
- 2010

The Newton polygon of the implicit equation of a rational plane curve is explicitly determined by the multiplicities of any of its parametrizations. We give an intersection-theoretical proof of this… (More)

- José I. Burgos Gil, Martín Sombra
- Discrete & Computational Geometry
- 2011

We study the problem of when the collection of the recession cones of a polyhedral complex forms also a complex. We exhibit an example showing that this is no always the case. We also show that if… (More)

- Francesco Amoroso, Louis Leroux, Martín Sombra
- Foundations of Computational Mathematics
- 2015

We show that, for a system of univariate polynomials given in the sparse encoding, we can compute a single polynomial de ning the same zero set, in time quasi-linear in the logarithm of the degree.… (More)

- Martín Sombra
- 2012

We propose an alternative definition of sparse resultants as resultants of multiprojective cycles in a suitable toric variety. This definition differs from the classical one in the sense that in our… (More)