J.E. Morais
Universidad Pública de Navarra
10 Papers
37 Citations
J.E. Morais is an academic researcher from Universidad Pública de Navarra. The author has contributed to research in topics: Polynomial & Hilbert series and Hilbert polynomial. The author has an hindex of 8, co-authored 10 publications. Previous affiliations of J.E. Morais include University of Cantabria.
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Papers
Straight--Line Programs in Geometric Elimination Theory
TL;DR: A new method for solving symbolically zero-dimensional polynomial equation systems in the affine and toric case using Newton iteration in order to simplify straight-line programs occurring in elimination procedures and improving the well-know worst-case complexity bounds for zero- dimensional equation solving in symbolic and numeric computing.
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Lower bounds for diophantine approximations
TL;DR: An intrinsic lower bound for the logarithmic height of diophantine approximations to a given solution of a zero-dimensional polynomial equation system is obtained and represents a multivariate version of Liouville's classical theorem on approximation of algebraic numbers by rationals.
138
When Polynomial Equation Systems Can Be Solved Fast
TL;DR: It is possible to solve any affine or toric zero-dimensional equation system in non-uniform sequential time which is polynomial in the length of the input description and the “geometric degree” of the equation system.
135
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Lower Bounds for diophantine Approximation
TL;DR: An intrinsic lower bound for the logarithmic height of diophantine approximations to a given solution of a zero--dimensional polynomial equation system is obtained and represents a multivariate version of Liouville's classical theorem on approximation of algebraic numbers by rationals.
69
On the intrinsic complexity of the arithmetic Nullstellensatz
TL;DR: An algorithmic procedure computing the polynomials and constants occurring in a Bezout identity, whose complexity is polynomial in the geometric degree and linear in the height of the system, is shown.
41