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Publications Influence

Real algebraic geometry

- J. Bochnak, M. Coste, M. Roy
- Mathematics
- 1992

1. Ordered Fields, Real Closed Fields.- 2. Semi-algebraic Sets.- 3. Real Algebraic Varieties.- 4. Real Algebra.- 5. The Tarski-Seidenberg Principle as a Transfer Tool.- 6. Hilbert's 17th Problem.… Expand

1,718 134- PDF

Algorithms in real algebraic geometry

- S. Basu, R. Pollack, M. Roy
- Mathematics
- 2003

Algebraically Closed Fields.- Real Closed Fields.- Semi-Algebraic Sets.- Algebra.- Decomposition of Semi-Algebraic Sets.- Elements of Topology.- Quantitative Semi-algebraic Geometry.- Complexity of… Expand

934 113- PDF

On the combinatorial and algebraic complexity of quantifier elimination

- S. Basu, R. Pollack, M. Roy
- Mathematics, Computer Science
- JACM
- 1 November 1996

TLDR

346 27- PDF

Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)

- S. Basu, R. Pollack, M. Roy
- Mathematics
- 1 August 2006

287 21

Zeros, multiplicities, and idempotents for zero-dimensional systems

- M. E. Alonso, E. Becker, M. Roy, T. Wörmann
- Mathematics
- 1 September 1996

We want to propose alternative computational methods for dealing with the following three classical problems in the study of zero-dimensional systems, rephrased in the context of finite-dimensional… Expand

106 8- PDF

Sylvester-Habicht Sequences and Fast Cauchy Index Computation

- Thomas Lickteig, M. Roy
- Computer Science, Mathematics
- J. Symb. Comput.
- 1 March 2001

TLDR

116 8- PDF

Dynamical method in algebra: effective Nullstellensätze

- M. Coste, H. Lombardi, M. Roy
- Mathematics, Computer Science
- Ann. Pure Appl. Log.
- 30 August 2001

TLDR

112 8- PDF

COMPUTING ROADMAPS OF SEMI-ALGEBRAIC SETS ON A VARIETY

- S. Basu, R. Pollack, M. Roy
- Mathematics
- 20 July 1999

Let R be a real closed field, Z(Q) a real algebraic variety defined as the zero set of a polynomial Q ∈ R[X1, . . . , Xk] and S a semi-algebraic subset of Z(Q), defined by a Boolean formula with… Expand

98 6- PDF

Finding at Least One Point in Each Connected Component of a Real Algebraic Set Defined by a Single Equation

- F. Rouillier, M. Roy, M. S. E. Din
- Computer Science, Mathematics
- J. Complex.
- 1 December 2000

TLDR

91 6- PDF

Sur la complexité du principe de Tarski-Seidenberg

- J. Heintz, M. Roy, P. Solernó
- Mathematics, Art
- 1989

1. I n t r o d u c t i o n Nous remercions Teresa Krick et Henri Lombardi pour l'aide qu'ils nous ont apportée et leurs nombreuses suggestions utiles concernant ce travail. Avant d'énoncer plus… Expand

136 5- PDF