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We present a new method for solving symbolically zero--dimensional polynomial equation systems in the affine and toric case. The main feature of our method is the use of problem adapted data… (More)

- Bernd Bank, Marc Giusti, Joos Heintz, Luis M. Pardo
- J. Complexity
- 2005

Let V be a closed algebraic subvariety of the n-dimensional projective space over the complex or real numbers and suppose that V is non-empty and equidimensional. The classic notion of a polar… (More)

- Bernd Bank, Marc Giusti, Joos Heintz, Luis M. Pardo
- Kybernetika
- 2004

Let $W$ be a closed algebraic subvariety of the $n$-dimensional projective space over the complex or real numbers and suppose that $W$ is non-empty and equidimensional. In this paper we generalize… (More)

We present sharp estimates for the degree and the height of the polynomials in the Nullstellensatz over $\Z$. The result improves previous work of Philippon, Berenstein-Yger and Krick-Pardo.
We also… (More)

- Marc Giusti, Joos Heintz, Jose Enrique Morais, Luis M. Pardo
- AAECC
- 1995

We present a new method for solving symbolically zero-dimensional polynomial equation systems in the affine and toric case. The main feature of our method is the use of an alternative data structure:… (More)

The procedures to solve algebraic geometry elimination problems have usually been designed from the point of view of commutative algebra. For instance, let us consider the problem of deciding whether… (More)

- Carlos Beltrán, Luis M. Pardo
- Foundations of Computational Mathematics
- 2011

We prove a new complexity bound, polynomial on the average, for the problem of finding an approximate zero of systems of polynomial equations. The average number of Newton steps required by this… (More)

- Luis M. Pardo
- AAECC
- 1995

- D. Castro, Luis M. Pardo, Klemens Hägele, Jose Enrique Morais
- J. Complexity
- 1999

In this extended abstract we deal with the relations between the numerical/diophantine approximation and the symbolic/algebraic geometry approachs to solving of multivariate diophentine polynomial… (More)

Abstract We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the… (More)