Roy, M.F (MarieFrançoise)
Overview
Works:  96 works in 235 publications in 3 languages and 3,415 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Author of introduction, Editor, Contributor, Thesis advisor, htt, Other, Interviewee, Publishing director, Opponent, Redactor, Publisher, Honoree 
Classifications:  QA564, 516.35 
Publication Timeline
.
Most widely held works by
M.F Roy
Algorithms in real algebraic geometry by
Saugata Basu(
)
29 editions published between 2003 and 2010 in English and held by 787 WorldCat member libraries worldwide
The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semialgebraic set appear frequently in many areas of science and engineering. In this firstever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects, and researchers in computer science and engineering will find the required mathematical background. Being selfcontained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semialgebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added
29 editions published between 2003 and 2010 in English and held by 787 WorldCat member libraries worldwide
The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semialgebraic set appear frequently in many areas of science and engineering. In this firstever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects, and researchers in computer science and engineering will find the required mathematical background. Being selfcontained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semialgebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added
An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem by
Henri Lombardi(
)
8 editions published between 1920 and 2020 in English and held by 535 WorldCat member libraries worldwide
"We prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely we express a nonnegative polynomial as a sum of squares of rational functions, and we obtain as degree estimates for the numerators and denominators the following tower of five exponentials 222d4k where d is the degree and k is the number of variables of the input polynomial. Our method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely we give an algebraic certificate of the emptyness of the realization of a system of sign conditions and we obtain as degree bounds for this certificate a tower of five exponentials, namely 2²(2max{2,d}4k+s2kmax{2,d}16kbit(d)) where d is a bound on the degrees, s is the number of polynomials and k is the number of variables of the input polynomials
8 editions published between 1920 and 2020 in English and held by 535 WorldCat member libraries worldwide
"We prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely we express a nonnegative polynomial as a sum of squares of rational functions, and we obtain as degree estimates for the numerators and denominators the following tower of five exponentials 222d4k where d is the degree and k is the number of variables of the input polynomial. Our method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely we give an algebraic certificate of the emptyness of the realization of a system of sign conditions and we obtain as degree bounds for this certificate a tower of five exponentials, namely 2²(2max{2,d}4k+s2kmax{2,d}16kbit(d)) where d is a bound on the degrees, s is the number of polynomials and k is the number of variables of the input polynomials
Real algebraic geometry : proceedings of the conference held in Rennes, France, June 2428, 1991 by
M Coste(
Book
)
23 editions published between 1992 and 2008 in English and held by 490 WorldCat member libraries worldwide
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade  see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years. R. Parimala: Algebraic and topological invariants of real algebraic varieties. Polotovskii, G.M.: On the classification of decomposing plane algebraic curves. Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results. Shustin, E.L.: Topology of real plane algebraic curves. Silhol, R.: Moduli problems in real algebraic geometry. Further contributions by: S. Akbulut and H. King; C. Andradas and J. Ruiz; A. Borobia; L. Br
23 editions published between 1992 and 2008 in English and held by 490 WorldCat member libraries worldwide
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade  see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years. R. Parimala: Algebraic and topological invariants of real algebraic varieties. Polotovskii, G.M.: On the classification of decomposing plane algebraic curves. Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results. Shustin, E.L.: Topology of real plane algebraic curves. Silhol, R.: Moduli problems in real algebraic geometry. Further contributions by: S. Akbulut and H. King; C. Andradas and J. Ruiz; A. Borobia; L. Br
Real algebraic geometry by
J Bochnak(
Book
)
4 editions published in 1998 in English and held by 373 WorldCat member libraries worldwide
"This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and uptodate research topics."
4 editions published in 1998 in English and held by 373 WorldCat member libraries worldwide
"This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and uptodate research topics."
Géométrie algébrique réelle by
J Bochnak(
Book
)
13 editions published in 1987 in 3 languages and held by 364 WorldCat member libraries worldwide
13 editions published in 1987 in 3 languages and held by 364 WorldCat member libraries worldwide
Algorithms in real algebraic geometry by
Saugata Basu(
Book
)
1 edition published in 2003 in English and held by 182 WorldCat member libraries worldwide
"Being selfcontained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students."Jacket
1 edition published in 2003 in English and held by 182 WorldCat member libraries worldwide
"Being selfcontained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students."Jacket
Real algebraic geometry by
J Bochnak(
Book
)
6 editions published between 1998 and 2011 in English and held by 74 WorldCat member libraries worldwide
A systematic treatment of real algebraic geometry. The accounts provided discuss both basic concepts and research topics, and may be used as a text for a graduate course
6 editions published between 1998 and 2011 in English and held by 74 WorldCat member libraries worldwide
A systematic treatment of real algebraic geometry. The accounts provided discuss both basic concepts and research topics, and may be used as a text for a graduate course
Real Algebraic Geometry : Proceedings of the Conference held in Rennes, France, June 2428, 1991 by
M Coste(
)
2 editions published in 1992 in English and held by 72 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 72 WorldCat member libraries worldwide
Géométrie Algébrique Réelle et Formes Quadratiques : Journées S.M.F., Université de Rennes 1, Mai 1981 by
J.L ColliotThélène(
)
2 editions published in 1982 in French and English and held by 72 WorldCat member libraries worldwide
2 editions published in 1982 in French and English and held by 72 WorldCat member libraries worldwide
Mathématique du collège au lycée ... by
Annie Berté(
Book
)
2 editions published in 1996 in French and held by 71 WorldCat member libraries worldwide
2 editions published in 1996 in French and held by 71 WorldCat member libraries worldwide
Real algebraic geometry by
J Bochnak(
Book
)
4 editions published between 1998 and 2010 in English and held by 36 WorldCat member libraries worldwide
4 editions published between 1998 and 2010 in English and held by 36 WorldCat member libraries worldwide
René Thom (19232002)(
Book
)
1 edition published in 2005 in French and held by 32 WorldCat member libraries worldwide
1 edition published in 2005 in French and held by 32 WorldCat member libraries worldwide
Géométrie algébrique réelle et formes quadratiques : journées S.M.F., Université de Rennes 1, Mai 1981 by
J.L ColliotThélène(
)
7 editions published between 1982 and 2006 in English and French and held by 32 WorldCat member libraries worldwide
7 editions published between 1982 and 2006 in English and French and held by 32 WorldCat member libraries worldwide
Colloque d'Algèbre by
Rennes> Colloque d'Algèbre. <1985(
Book
)
7 editions published in 1985 in French and English and held by 21 WorldCat member libraries worldwide
7 editions published in 1985 in French and English and held by 21 WorldCat member libraries worldwide
Géométrie algébrique réelle by
J Bochnak(
Book
)
1 edition published in 1987 in French and held by 21 WorldCat member libraries worldwide
1 edition published in 1987 in French and held by 21 WorldCat member libraries worldwide
Mathématiques et robotique : journée annuelle de la Société mathématique de France, samedi 1 juin 1991 by
Société mathématique de France(
Book
)
5 editions published between 1991 and 1997 in French and Undetermined and held by 18 WorldCat member libraries worldwide
5 editions published between 1991 and 1997 in French and Undetermined and held by 18 WorldCat member libraries worldwide
Mathematics, algorithms, proofs 05021 abstracts collection ; Dagstuhl seminar(
)
1 edition published in 2006 in English and held by 17 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 17 WorldCat member libraries worldwide
Subdiscriminant of symmetric matrices are sums of squares(
)
1 edition published in 2006 in English and held by 17 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 17 WorldCat member libraries worldwide
Selecting a MAPLE research reactor core for 110 MW operation = Choix d'un coeur de réacteur de recherches de la catégorie
MAPLE pour une puissance de coeur de 110 MW by
H. J Smith(
Book
)
4 editions published in 1986 in English and held by 13 WorldCat member libraries worldwide
4 editions published in 1986 in English and held by 13 WorldCat member libraries worldwide
Real Algebraic Geometry by
J Bochnak(
)
2 editions published in 1998 in English and held by 11 WorldCat member libraries worldwide
The present volume is a translation, revision and updating of our book (pubƯ lished in French) with the title "Geometrie Algebrique Reelle". Since its pubƯ lication in 1987 the theory has made advances in several directions. There have also been new insights into material already in the French edition. Many of these advances and insights have been incorporated in this English version of the book, so that it may be viewed as being substantially different from the original. We wish to thank Michael Buchner for his careful reading of the text and for his linguistic corrections and stylistic improvements. The initial Jb. TEiX file was prepared by Thierry van Effelterre. The three authors participate in the European research network "Real Algebraic and Analytic Geometry". The first author was partially supported by NATO Collaborative Research Grant 960011. Jacek Bochnak April 1998 Michel Coste MariePranroise Roy Table of Contents Preface. ... ... ... ... ... V Introduction. ... ... ... ... . 1 1. Ordered Fields, Real Closed Fields ... ... . 7 1. 1 Ordered Fields, Real Fields ..." ... ... . 7 1. 2 Real Closed Fields. ... ... ... . 9 1. 3 Real Closure of an Ordered Field. ... ... 14 1. 4 The TarskiSeidenberg Principle. ... ... . 17 2. Semialgebraic Sets ... ... ... ... 23 2. 1 Algebraic and Semialgebraic Sets. ... ... . 23 2. 2 Projection of Semialgebraic Sets. Semialgebraic Mappings. . 26 2. 3 Decomposition of Semialgebraic Sets. ... ... . 30 2. 4 Connectedness. ... ... ... ... 34 2. 5 Closed and Bounded Semialgebraic Sets. Curveselection Lemma ... ... ... ... 35 2. 6 Continuous Semialgebraic Functions. Lojasiewicz's Inequality 42 2. 7 Separation of Closed Semialgebraic Sets. ...
2 editions published in 1998 in English and held by 11 WorldCat member libraries worldwide
The present volume is a translation, revision and updating of our book (pubƯ lished in French) with the title "Geometrie Algebrique Reelle". Since its pubƯ lication in 1987 the theory has made advances in several directions. There have also been new insights into material already in the French edition. Many of these advances and insights have been incorporated in this English version of the book, so that it may be viewed as being substantially different from the original. We wish to thank Michael Buchner for his careful reading of the text and for his linguistic corrections and stylistic improvements. The initial Jb. TEiX file was prepared by Thierry van Effelterre. The three authors participate in the European research network "Real Algebraic and Analytic Geometry". The first author was partially supported by NATO Collaborative Research Grant 960011. Jacek Bochnak April 1998 Michel Coste MariePranroise Roy Table of Contents Preface. ... ... ... ... ... V Introduction. ... ... ... ... . 1 1. Ordered Fields, Real Closed Fields ... ... . 7 1. 1 Ordered Fields, Real Fields ..." ... ... . 7 1. 2 Real Closed Fields. ... ... ... . 9 1. 3 Real Closure of an Ordered Field. ... ... 14 1. 4 The TarskiSeidenberg Principle. ... ... . 17 2. Semialgebraic Sets ... ... ... ... 23 2. 1 Algebraic and Semialgebraic Sets. ... ... . 23 2. 2 Projection of Semialgebraic Sets. Semialgebraic Mappings. . 26 2. 3 Decomposition of Semialgebraic Sets. ... ... . 30 2. 4 Connectedness. ... ... ... ... 34 2. 5 Closed and Bounded Semialgebraic Sets. Curveselection Lemma ... ... ... ... 35 2. 6 Continuous Semialgebraic Functions. Lojasiewicz's Inequality 42 2. 7 Separation of Closed Semialgebraic Sets. ...
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Audience Level
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Related Identities
 Coste, M. (Michel) Other Author Editor
 Basu, Saugata 1968 Author
 Pollack, Richard
 Bochnak, J. (Jacek) Author
 Mahé, Louis Other Editor
 Lombardi, Henri Publisher Author Contributor
 Perrucci, Daniel
 ColliotThélène, JeanLouis Author Editor Scientific advisor
 Berté, Annie Author
 Anné, Colette Editor
Useful Links
Associated Subjects
Algebra AlgebraData processing Algebraic fields Algebraic number theory Algorithms Commutative algebra Control theory Forms, Quadratic Functions of real variables Geometry, Algebraic Geometry, AlgebraicData processing Mathematics Mixed oxide fuels (Nuclear engineering) Nuclear reactorsCores Polynomials Recursive functions Robotics RoboticsMathematics RobotsMotion Uranium compounds
Covers
Alternative Names
CosteRoy, M.F.
CosteRoy, M.F. (MarieFrançoise)
CosteRoy, M.F (MarieFrançoise), 1950
CosteRoy, MarieFrançoise
MarieFrançoise Roy Frans wiskundige
MarieFrançoise Roy fransk matematiker
MarieFrançoise Roy französische Mathematikerin
MarieFrançoise Roy French mathematician & academic
MarieFrançoise Roy French mathematician and academic
MarieFrançoise Roy matemática francesa
MarieFrançoise Roy mathématicienne et professeur d'université française
Roy, M.F.
Roy, M.F. 1950
Roy, M.F. (MarieFrançoise), 1950
Roy MarieFrançoise
Roy, MarieFrançoise, 1950
Roy MarieFrançoise Coste
Roy, MarieFrançoise Coste, 1950
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