Ouvrage

S. Basu, R. Pollack, M.-F. Roy. Algorithms in real algebraic geometry, revised and completed version of 2nd edition,  (2016)

S. Basu, R. Pollack, M.-F. Roy. Algorithms in real algebraic geometry, 2nd edition (2006)

S. Basu, R. Pollack, M.-F. Roy. Algorithms in real algebraic geometry. Berlin Heidelberg New York: Springer (2003)

J. Bochnak , M. Coste , M.-F. Roy. Real algebraic geometry. Second edition in english.Ergebnisse der Mat., vol. 36. Berlin Heidelberg New York: Springer (1998)

J. Bochnak , M. Coste , M.-F. Roy. Géométrie Algébrique Réelle. Ergebnisse der Mat., vol. 12. Berlin Heidelberg New York: (1987)

Article soumis

D. Perrucci, M.-F. Roy. Algebraic winding numbers (2023). (preliminary version, arXiv: 2305.08638 ).

Articles parus

D. Niang Diatta, S; Diatta, F. Rouillier, M.-F. Roy, M. Sagraloff. Bounds for polynomials on algebraic numbers and application to curve topology. Discrete Comput Geom 67, 631–697 (2022). (preliminary version, arXiv:1807.10622v3)

D. Perrucci, M.-F. Roy. A new general formula to compute the Cauchy Index with Subresultants in an interval, Special issue of the Journal of Symbolic Computation on the occasion of MEGA 2019, voume 108, March–April 2022, Pages 465-481 (preliminary version, arXiv:1812.02470v1).

S. Basu, M.-F. Roy. Quantitative Curve Selection Lemma, Math. Z (2021) https://doi.org/10.1007/s00209-021-02837-0 (preliminary version, arXiv:1803.00505).

H. Lombardi, D. Perrucci, M.-F. Roy. An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem (preliminary version, arXiv:1404.2338v3). Memoirs of the AMS, Vol 263, Number 1277, January 2020.

M.-F. Roy, A. Szpirglas. Sylvester double sums, subresultants and symmetric multivariate Hermite interpolation, Journal of Symbolic Computation, Volume 96, January–February 2020, Pages 85-107 (preliminary version, arXiv:1805.10609).

D. Perrucci, M.-F. Roy. Quantitative Fundamental Theorem of Algebra, The Quarterly Journal of Mathematics, Volume 70, Issue 3, September 2019, Pages 1009–1037 (preliminary version, arXiv:1803.04358).

D. Perrucci, M.-F. Roy. Elementary recursive quantifier elimination based on Thom encoding and sign determination. Annals of Pure and Applied Logic, Volume 168, Issue 8, August 2017, Pages 1588-1604 (preliminary version, arXiv:1609.02879v2) .

S. Basu, M.-F. Roy. Divide and Conquer Roadmaps for Algebraic sets, Discrete and Computational Geometry Volume 52 Issue 2 (September 2014) Pages 278-343   (preliminary version, arXiv:1305.3211)

S. Basu, M.-F. Roy, M. Safey El Din, E. Schost. A baby step-giant step roadmap algorithm for general algebraic sets, Foundation of Computational Mathematics : Volume 14, Issue 6 (2014), Page 1117-1172 (preliminary version, arXiv:1201.6439).

D. Perrucci, M.-F. Roy. Zero-nonzero and real-nonreal sign determination, Linear Algebra and Its Applications 439 (2013), no. 10, pp. 3016-3030 (preliminary version,arXiv:1305.4131)

M.-F. Roy, S. M. Sedjelmaci. New fast euclidean algorithm.  Journal of. Symbolic Computation, 50 (2013) 208-226 (preliminary version)

M.-F. Roy, A. Szpirglas. Sylvester double sums and subresultants,  Journal of Symbolic Computation, Volume 46, 4 (2011), 385–395 (preliminary version)

S. Basu, M.-F. Roy. Bounding the radii of balls meeting every connected component of semi-algebraic sets, Journal of Symbolic Computation 45 (2010) 1270-1279 (preliminary version, arXiv:0911.1340)

S. Basu, D.V. Pasechnik, M.-F. Roy.  Bounding the Betti numbers and computing the Euler-Poincare characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials. Journal of the European Mathematical Society (2010). 12(2), 529–553 (preliminary version, arXiv:0708.3522)

S. Basu, R. Pollack, M.-F. Roy. An asymptotically tight bound on the number of connected components of realizable sign conditions, Combinatorica 29 (5) (2009) 523-546 (preliminary version, arXiv:0603256)

S. Basu, D. Pasechnik, M.-F. Roy. Computing the Betti numbers and the Euler-Poincare characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials,  Journal of Algebra 321 (2009) 2206-2209 (preliminary version arXiv:0806.3911v1)

F. Boudaoud, F. Caruso, M.-F. Roy Certificates of positivity in the Bernstein basis,  Discrete and Computational Geometry 39 4 639-655 (2008)

S. Basu, R. Pollack, M.-F. Roy. Computing the First Betti Number of Semi-algebraic Sets, 8 (1) 97-136 FOCM (2008) (preliminary version, arXiv:0603248)

M. Coste, T. Lajous, H. Lombardi, M.-F. Roy. Generalized Budan-Fourier theorem and virtual roots, Journal of Complexity, 21, 478-486 (2005)

S. Basu, R. Pollack, M.-F. Roy. On the Betti Numbers of Sign Conditions,  Proceedings of the AMS,  133, 965-974 (2005)

S. Basu, R. Pollack, M.-F. Roy, Computing the Euler characteristic of sign conditions, Journal of Computational Complexity, 14, 53-71 (2005)

S. Basu, R. Pollack, M.-F. Roy. Computing the Dimension of a Semi-Algebraic Set. Zap. Nauchn. Semin. POMI 316 (2004). Journal of Mathematical Sciences 134, 2346–2353 (2006)

M.-F. Roy , N. Vorobjov. Computing the complexification of a semi-algebraic set, Math. Zeitschrift 239, 131-142 (2002)

T. Lickteig, M.-F. Roy. Sylvester-Habicht sequences and fast Cauchy index computations, Journal of Symbolic Computation, , 31 315-341 (2001)

M. Coste, H. Lombardi, M.-F. Roy. Dynamical method in algebra: effective Nullstellensatze, Annals of Pure and Applied Logic, 111, 203-256 (2001) arXiv:1701.05794

H. Lombardi, M.-F. Roy, M. Safey. New structure theorems for subresultants, Special Issue Symbolic Computation in Algebra, Analysis, and Geometry, Journal of Symbolic Computation, 29 663-690 (2000)

F. Rouillier, M.-F. Roy, M. Safey. Finding at least one point in each connected component of a real algebraic set defined by a single equation, Journal of Complexity 16 716-750 (2000)

S. Basu, R. Pollack, M.-F. Roy. Computing roadmaps of semi-algebraic sets on a variety,Journal of the AMS, VOL 3, 1 55-82 (1999)

S. Basu, R. Pollack ,M.-F. Roy. On Computing a Set of Points meeting every Cell Defined by a Family of Polynomials on a Variety, Journal of Complexity, 13 28-37 (1997)

T. Lickteig, M.-F. Roy. Semi-algebraic complexity of quotients and sign determinations of remanders , Journal of Complexity 12 (4) 545-571 (1996)

I. Itenberg, M.-F. Roy. Multivariate Descartes's rule Beitrage zur Algebra und Geometrie Volume 37 (1996) 2, 337-346

S. Basu, R. Pollack, M.-F. Roy. On the combinatorial and algebraic complexity of Quantifier elimination, J. A. C. M., 43, 1002--1045, (1996).

H. Lombardi, N. Mnev, M.-F. Roy. The Positivstellensatz and small deduction rules for systems of inequalities, Math. Nachr. 181 245-2259 (1996).

S. Basu, R. Pollack, M.-F. Roy. On the number of cells defined by a family of polynomials on a subvariety, Mathematika 43 120-126 (1996).

M.-F. Roy, N.N.Vorobjov. Finding irreducible components of some real transcendental varieties. Journal of Computationnal complexity 4 107-132 (1994)

J. Heintz, M.-F. Roy, P. Solerno. On the theoretical and practical complexity of the existential theory of the reals. The Computer Journal, vol 36, 5 427-431(1993).

J. Heintz, M.-F. Roy, P. Solerno. Description of the connected components of a semi-algebraic set in single exponential time Discrete and Computationnal Geometry 11 121-140 (1994).

F. Cucker, H. Laneau, B. Mishra, P. Pedersen, M.-F. Roy. NC algorithms for Real algebraic numbers.. Applicable Algebra in Engineering, 3: 79-98 (1992)

L. Gonzalez, H. Lombardi, T. Recio, M.-F. Roy. Spécialisation de la suite de Sturm. II Informatique théorique et applications 28 1-24 (1994).

J. Heintz, M.-F. Roy, P. Solerno. Sur la complexité du principe de Tarski-Seidenberg. Bulletin de la SMF 118 101-126 (1990).

F. Cucker, M.-F. Roy. A theorem on random polynomials and some consequences in average complexity . Journal of Symbolic Computation 10 (1990).

L. Gonzalez, H. Lombardi, T. Recio, M.-F. Roy. Sous-résultants et spécialisation de la suite de Sturm. I I. Informatique théorique et applications 24 561-588 (1990).

M. Coste, M.-F. Roy. Encore une démonstration de l'existence de stratifications avec lacondition w. Bulletin of the Polish Academy of Science 37 597-601 (1989) .

M.-F. Roy, A. Szpirglas. Complexity of the computations with real algebraic numbers. Journal of Symbolic computation 10 39-51 (1990).

M.-F. Roy. Computation of the topology of a real algebraic curve. Astérisque 192 (1990)17-33.

M. Coste, M.-F. Roy. Thom's lemma, the coding of real algebraic numbers and thetopology of semi-algebraic sets . Journal of Symbolic computation 5 121-130 (1988)

M. E. Alonso, M.-F. Roy. Real strict localisations. Math. Z. 194, 429-441 (1987)

M. Coste, M.-F. Roy. La topologie du spectre réel. Contemp. Math 8, 27-59 (1982).

M. Coste, M.-F. Roy. Le topos étale réel d'un anneau. Cahiers topologie géom. différentielle, 22, 19-24 (1981)

M. Coste, L. Mahé, M.-F. Roy. Contribution to the study of the natural number object in a topos. J. Pure Appl. Algebra 17, 35-68 (1980)

Thèse

M.-F. Roy. Spectre réel d'un anneau et topos étale réel. Thèse d'état, Université Paris-Nord (1980)

Articles de synthèse

M.-F. Roy,, Quantitative results on quadratic semi-algebraic sets, dans "Electronic Notes in Discrete Mathematics", vol. 31, 129 p., DOI : 10.1016/j.endm.2008.06.026

M.-F. Roy, Géométrie et syntaxe: les ensembles semi-algébriques et leurs généralisations, Géométrie au XXème siècle, Histoire et Horizons, Hermann, 463-468, (2005).

M.-F. Roy, Some recent quantitative and algorithmic results in real algebraic geometry, 737-750, Goodman/Pollack Festschrift, Springer (2003) .

M.-F. Roy, Formes et formules: les algorithmes de la géométrie algébrique réelle, 53-63 dans Calculs et formes : de l'activité mathématique, Jacqueline Boniface ed., Ellipses (2003)

M.-F. Roy, Three problem in real algeraic geometry and their descendants, 991-1002, Mathematics unlimited, 2001 and Beyond, Springer Verlag (2001)

M.-F. Roy. Géométrie algébrique réelle, Development of Mathematics 1950-2000 , 939-966, Birkhauser (2000)

I. Itenberg, M.-F. Roy. Interactions between real algebraic geometry and discrete and computational geometry, Advances in Discrete and Computational Geometry, AMS, Contemporary mathematics 223 217-236 (1999)

J. Mainguené, .M-F. Roy. Démonstration automatique en géométrie, une approche par la géométrie analytique, Bulletin de l'APMEP n° 421 Mars -avril (1999)

M.-F. Roy. Basic algorithms in real algebraic geometry: from Sturm theorem to the existential theory of reals, Lectures on Real Geometry in memoriam of Mario Raimondo, de Gruyter Expositions in Mathematics 23, 1-67 (1996)

M.-F. Roy. Computations in Real Algebraic Geometry, Summer Seminar " Mathematics of Numerical Anlysis: Real number algorithms " (Park City 1995), AMS Conference in Applied mathematics. Lectures in Applied Mathematics 32 701-713(1996)

M.-F. Roy. Géométrie algébrique réelle et robotique: la complexité du déménagement des pianos. Gazette des Mathematiciens, janvier 1992.

J.Heintz, T. Krick, M.-F. Roy, P. Solerno. Geometric problems solvable in single exponential time. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (S.Sakata Ed.), Lecture Notes in Comput. Sci. 508, Springer Berlin 11-23 (1991)

J. Heintz, T. Recio, M.-F. Roy. Algorithms in real algebraic geometry and applications to computational geometry. DIMACS Series in Discrete and Computational Mathematics. AMS 137-163 (1991)

M.-F. Roy. Logique et géométrie algébrique réelle. dans: Logic Colloquim '85, 267-279. Amsterdam: North-Holland 1987.

Chapitres de livres

L. Gonzalez-Vega, F. Rouillier, M.-F. Roy. Symbolic Recipes for Polynomial System Solving, In: Some tapas of computer algebra, A. Cohen et al. ed. Springer, 34-65 (1999).

L. Gonzalez-Vega, F. Rouillier, M.-F. Roy, G. Trujillo. Symbolic Recipes for Real Solutions In: Some tapas of computer algebra, A. Cohen et al. ed. Springer, 121-167 (1999).

Textes acceptés comme communications à des congrès internationaux

G. Butcher, M.-H. Chiu, I. Gledhill, R. Ivie, S. P. Dawson, M.-F. Roy. An international and interdisciplinary project to analyze and help reduce the gender gap in mathematics and the natural sciences. In WOMEN IN PHYSICS : 6th IUPAP International Conference on Women in Physics, volume 2109 of WOMEN IN PHYSICS : 6th IUPAP International Conference on Women in Physics, page 030006 (2019).

D. Perrucci, M.-F. Roy. A new general formula to compute the Cauchy Index with Subresultants in an interval, accepted at MEGA 2019 (preliminary version, arXiv:1812.02470v1)?

D. Niang Diatta, F. Rouillier, M.-F. Roy. On the computation of the topology of plane curves, accepted at ISSAC 2014 (preliminary version,hal-00935728 v2).

S. Basu R. Pollack M.-F. Roy. Computing the first Betti number and the connected components of semi-algebraic sets. Accepté à STOC 2005.

S. Basu R. Pollack M.-F. Roy. Computing connected components of semi-agebraic sets, ISSACC 98

S. Basu R. Pollack M.-F. Roy. Computing Roadmaps of Semi-algebraic Sets on a Variety, Foundations of Computational Mathematics. F. Cucker and M. Shub, Eds., 1--15,1997.

S. Basu R. Pollack M.-F. Roy. Computing Roadmaps of Semi-algebraic Sets, Proc. 28 Annual ACM Symposium on the Theory of Computing, 168-173, 1996.

M.-F. Roy, N. Vorobjov. Computing the complexification of a semi-algebraic set, ISSACC 96 Proceedings 26-39 (1996).

S. Basu R. Pollack M.-F. Roy. On the combinatorial and algebraic complexity of Quantifier elimination, Proc. 11 th IEEE Symp. On Foundations of Computer Science, 1994, 632-641.

S. Basu, R. Pollack, M.-F. Roy. A new algorithm to find a point in every cell defined by a family of polynomials. Quantifier Elimination and Cylrindical Algebraic Decomposition, Texts and Mongraphs in Symbolic Computation, B. Caviness and J. Johnson, Eds. , Springer 341-350 (1998)

L. Gonzalez, H. Lombardi, T. Recio, M.-F. Roy. Sturm-Habicht,determinants and real roots of univariate polynomials. . Quantifier Elimination and Cylrindical Algebraic Decomposition, Texts and Mongraphs in Symbolic Computation, B. Caviness and J. Johnson, Eds. Springer 300-316 (1998)

M.-E. Alonso, E. Becker, M.-F. Roy, T. Wormann. Zeroes, Multiplicities and Idempotents for Zerodimensional Systems , Algorihtms in algebraic geometry and applications, Progress in Mathematics, vol 143. Birkhauser (1996) 1-16

M.-F. Roy, T. Van Effelterre. Aspects graphs of bodies of revolution with algorithms of real algebraic geometry. Algorihtms in algebraic geometry and applications, Progress in Mathematics, vol 143. Birkhauser (1996) 353-364

E. Becker, J.-P. Cardinal, M.-F. Roy, Z. Szafraniec. Multivariate Bezoutians, Kronecker Symbol and Eisenbud-Levine formula. Algorihtms in algebraic geometry and applications, Progress in Mathematics, vol 143. Birkhauser (1996) 79-104

A. Guergueb, J. Mainguené, M.-F. Roy. Examples of automatic theorem proving in real geometry. ISSACC 94.

M.-F. Roy, T. Van Effelterre. Aspect graphs of algebraic surfaces. ISSACC 93.

P. Pedersen, M.-F. Roy, A. Szpirglas. Counting real zeroes in the multivariate case. Dans Computational algebraic geometry, Eyssette et Galligo ed. Progress in Mathematics 109 , 203-224, Birkhaüser (1993).

J. Heintz, M.-F. Roy, P. Solerno. Single exponential path finding in semi-algebraic sets I: The case of regular bounded hypersurface. Discrete and Applied Math., Proc.AAECC-8 Tokyo, 1990; Lectures Notes in Comp. Sci. 508, Springer-Verlag (1991) 180-186.

M.-F. Roy, A. Szpirglas. Sign determinations on zero-dimensional sets. Actes de MEGA 90,Progress in Mathematics 34 457-468, Birkhaüser (1991)

H. Lombardi, M.-F. Roy. Elementary constructive theory of ordered fields. Actes de MEGA 90, Progress in Mathematics 34 249-262 Birkhaüser (1991).

J. Heintz, M.-F. Roy, P. Solerno. On the complexity of semi-algebraic sets.293-298 IFIP'89 San Francisco, North-Holand (1989)

L. Gonzalez, H. Lombardi, T. Recio, M.-F. Roy. Sturm-Habicht sequence. 136-145, ISSAC'89 Portland, ACM Press.

F. Cucker, L. M. Pardo Vassallo , M. Raimondo , T. Recio, M.-F. Roy Computation of the real analytic components of a real algebraic curve . (Actes de la Conférence A.A.E.C.C.-5, Minorca). Springer Lecture Notes in Computer Science 356 161-182 (1989).

Articles dans des volumes

D. Niang Diatta, S. Diatta, M.-F. Roy. Quantitative Result on the Deviation of a Real Algebraic Curve from Its Vertical Tangents. In: Seck D., Kangni K., Nang P., Salomon Sambou M. (eds) Nonlinear Analysis, Geometry and Applications. Trends in Mathematics. Birkhäuser, Cham (2020).

H. Mihaljevic, M.-F. Roy. A data analysis of women's trails among ICM speakers (preliminary version arXiv:1903.02543v2). C. Araujo et als (eds.). World Meeting for Women in Mathematics 2018. Association for Women in Matematics Series, Volume 20, Springer, 111-128 (2019).

S. Basu, R. Pollack, M.-F. Roy. Betti number bounds, Applications and Algorithms. Current trends in combinatorial and computational geometry. Cambridge University Press. Special volume devoted to special program. "Discrete and Computational Geometry" at MSRI in its series `Mathematical Sciences Research Institute Publications' 52 87-96 (2005).

B. Mourrain, F. Rouillier, M.-F. Roy. The Berstein basis and real root isolation. Current trends in combinatorial and computational geometry. Cambridge University Press. Special volume devoted to special program. "Discrete and Computational Geometry" at MSRI in its series `Mathematical Sciences Research Institute Publications' 52 459-478 (2005).

T. Coquand, H. Lombardi, M.-F. Roy. An elementary characterization of Krull dimension 239-244. Selected Articles from a Workshop in San Servolo, Venice, Italy, May 12--16, 2003.  Oxford Logic Guides, Oxford University Press (2005).

J. Heintz, M.-F. Roy, P. Solerno. Single exponential path finding in semi-algebraic sets II: The general case. Algebraic geometry and its applications. Bajaj editor, Springer Verlag (1993) 467-481.

M.-F. Roy, A. Szpirglas. Complexity of the computation of cylindrical algebraic decomposition and topology of curves, using Thom's lemma. Actes de la rencontre de géométrie algébrique réelle de Trento, 1988, Springer Lecture Notes in Mathematics 1420 223-236 (1990) .

D. Duval, M.-F. Roy. Curves and computer algebra. Springer Lecture Notes in Computer Science 391 28-42 (1989).

M.-F.Roy. Fonctions de Nash et faisceau structural sur le spectre réel. Dans: Géométrie algébrique réelle et formes quadratiques, 406-432. Lecture Notes in Math. vol. 959. Berlin Heidelberg. NewYork: Springer 1982 .

Autres rencontres scientifiques

M.-F. Roy, The role of Hilbert problems in real algebraic geometry. European Women in Mathematics, Proceedings of the 9th general meeting 189-200, Hindawi (2000).

S. Basu, R. Pollack, M.-F. Roy. Computing a Set of Points meeting every Cell Defined by a Family of Polynomials on a Variety, WAFR, 94, Algorithmic foundations of robotics A K Peters 537-555.

Compte-rendus à l'Académie des Sciences

R. Pollack, M.-F. Roy. On the number of cells defined by a set of polynomials. C. R. Acad. Sci. Paris 316 573-577 (1993).

J. Heintz, M.-F. Roy, P. Solerno. Description des composantes connexes d'un ensemble semi-algébrique en temps simplement exponentiel. C. R. Acad. Sci. Paris 311 167-70 (1991).

Z. Ligatsikas, M.-F. Roy. Séries de Puiseux sur un corps réel clos. C. R. Acad. Sci. Paris 311 625-628 (1990).

D. Grigor'ev, J. Heintz, M.-F. Roy, P. Solerno, N. Vorobjov. Comptage des composantes connexes d'un ensemble semi-algébrique en temps simplement exponentiel. C. R. Acad. Sci. Paris 311 879-882 (1990).

J. Heintz, M.-F. Roy P. Solerno. Complexité du principe de Tarski-Seidenberg C.R.Acad. Sci. Paris 309 825-30 (1989).

J.-P. Dedieu, M.-F. Roy. Factorisation équimodulaire des polynômes à coefficients réels et calcul formel. C. R. Acad. Sc.309 519-522 (1989).

F. Cucker, M.F. Roy. Théorèmes des zéros et positivstellensatze pour les fonctions de Nash dans le cas non-lisse . C.R. Acad. Sci. Paris 303, 563-566 (1986)

M. Coste, M.-F. Roy. Le spectre réel d'un schéma affine est spatial. C. R. Ac. Sci. Paris 290, 91-94 (1980)

M.-F. Roy. Construction d'un modèle booléen de la théorie des ensembles à partir d'un opos booléen. C. R. Ac. Sci. Paris 278, 1073-1076 (1974)

Echanges culturels France-Niger

Nicole Moulin, Boubé Namaiwa, M-F. Roy, Bori Zamo. Lougou et Saraouniya, Collection Arewa, Tarbiyya Tatali, (2007), 2ème édition avec L'Harmattan (2017).

Mathématiques en Afrique

M-F. Roy. Les mathématiques dans le développement en Afrique, quelques réflexions (2007) pdf

Liste mise à jour le 7/12/2020