Edit Profile (opens in new tab) Lombardi, Henri Co-Author Distance Author ID: lombardi.henri Published as: Lombardi, Henri; Lombardi, H.; Lombardi, L. Henri more...less Homepage: http://hlombardi.free.fr/ External Links: MGP · dblp · IdRef · theses.fr Videos: carmin.tv Documents Indexed: 124 Publications since 1989, including 7 Books and 21 Additional arXiv Preprints 1 Contribution as Editor Co-Authors: 37 Co-Authors with 104 Joint Publications 621 Co-Co-Authors all top 5 Co-Authors 21 single-authored 27 Coquand, Thierry 23 Quitté, Claude 14 Neuwirth, Stefan 11 Gonzalez-Vega, Laureano 11 Roy, Marie-Françoise 10 Díaz-Toca, Gema María 10 Yengui, Ihsen 9 Alonso García, María Emilia 9 Labhalla, Salah 4 Mahboubi, Assia 4 Perdry, Hervé 4 Schuster, Peter Michael 3 Galligo, André 3 Kuhlmann, Franz-Viktor 3 Recio, Tomas 2 Barhoumi, Sami 2 Coste, Michel 2 Ducos, Lionel 2 Emiris, Ioannis Z. 2 Hibti, M. 2 Legeard, Bruno 1 Abdeljaoued, Jounaïdi 1 Ben Atti, Nadia 1 Delzell, Charles N. 1 Ellouz, Afef 1 Gamanda, Maroua 1 Khalouani, Mohamed 1 Lajous-Loaeza, Tomás 1 Mahé, Louis 1 Marlin, Roger 1 Mnëv, Nikolai Evgen’evich 1 Moutai, E. 1 Perrucci, Daniel 1 Roy, Marie-France 1 Safey El Din, Mohab 1 Salou, M. 1 Tête, Claire all top 5 Serials 8 Journal of Algebra 7 Journal of Pure and Applied Algebra 5 Journal of Symbolic Computation 5 Mathematical Logic Quarterly (MLQ) 4 Theoretical Computer Science 4 Annals of Pure and Applied Logic 3 Mathematische Zeitschrift 3 Comptes Rendus de l’Académie des Sciences. Série I 3 RAIRO. Informatique Théorique et Applications 3 Mathématiques en Devenir 2 Communications in Algebra 2 Mathematische Nachrichten 1 American Mathematical Monthly 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Acta Arithmetica 1 Archiv der Mathematik 1 Collectanea Mathematica 1 Manuscripta Mathematica 1 Memoirs of the American Mathematical Society 1 Journal of Complexity 1 SIAM Journal on Matrix Analysis and Applications 1 Mathematical Structures in Computer Science 1 Linear Algebra and its Applications 1 Applicable Algebra in Engineering, Communication and Computing 1 Publications Mathématiques de la Faculté des Sciences de Besançon. Théorie des Nombres 1 Bulletin des Sciences Mathématiques 1 Annals of Mathematics and Artificial Intelligence 1 Quadrature 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 La Gaceta de la Real Sociedad Matemática Española 1 Cahiers de Topologie et Géométrie Différentielle Catégoriques 1 Journal of Algebra and its Applications 1 International Journal of Commutative Rings 1 Mathématiques & Applications (Berlin) 1 Algebra and Applications 1 Actes des Rencontres du C.I.R.M. 1 Références Sciences all top 5 Fields 70 Commutative algebra (13-XX) 65 Mathematical logic and foundations (03-XX) 34 Field theory and polynomials (12-XX) 34 Algebraic geometry (14-XX) 22 Computer science (68-XX) 10 Order, lattices, ordered algebraic structures (06-XX) 8 Number theory (11-XX) 6 Numerical analysis (65-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 \(K\)-theory (19-XX) 5 Real functions (26-XX) 3 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Approximations and expansions (41-XX) 1 General topology (54-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 85 Publications have been cited 782 times in 358 Documents Cited by ▼ Year ▼ Dynamical method in algebra: Effective Nullstellensätze. Zbl 0992.03076 Coste, Michel; Lombardi, Henri; Roy, Marie-Françoise 57 2001 Certified approximate univariate GCDs. Zbl 0891.65015 Emiris, Ioannis Z.; Galligo, André; Lombardi, Henri 56 1997 Commutative algebra: constructive methods. Finite projective modules. Translated from the French by Tania K. Roblot. Zbl 1327.13001 Lombardi, Henri; Quitté, Claude 52 2015 Hidden constructions in abstract algebra: Krull dimension of distributive lattice and commutative rings. Zbl 1096.13507 Coquand, Thierry; Lombardi, Henri 41 2003 A logical approach to abstract algebra. Zbl 1118.03059 Coquand, Thierry; Lombardi, Henri 28 2006 Commutative algebra. Constructive methods. Finite type projective modules. Course and exercises. (Algèbre commutative. Méthodes constructives. Modules projectifs de type fini. Cours et exercices.) Zbl 1242.13002 Lombardi, Henri; Quitté, Claude 27 2011 Sturm-Habicht sequences, determinants and real roots of univariate polynomials. Zbl 0900.12002 González-Vega, L.; Recio, T.; Lombardi, H.; Roy, M.-F. 26 1998 Krull dimension, Nullstellensätze and dynamical evaluation. (Dimension de Krull, Nullstellensätze et évaluation dynamique.) Zbl 1095.13517 Lombardi, Henri 25 2002 Spécialisation de la suite de Sturm et sous-résultants. I. (Specialization of the Sturm sequence and subresultants. I). Zbl 0732.68059 González-Vega, L.; Lombardi, H.; Recio, T.; Roy, M.-F. 24 1990 Generating non-Noetherian modules constructively. Zbl 1059.13006 Coquand, Thierry; Lombardi, Henri; Quitté, Claude 24 2004 New structure theorem for subresultants. Zbl 0973.12007 Lombardi, Henri; Roy, Marie-Françoise; El Din, Mohab Safey 21 2000 Algorithmic theory of arithmetic rings, Prüfer rings and Dedekind rings. (Théorie algorithmique des anneaux arithmétiques, des anneaux de Prüfer et des anneaux de Dedekind.). Zbl 1093.13015 Ducos, L.; Lombardi, H.; Quitté, C.; Salou, M. 20 2004 Hidden constructions in abstract algebra: The local-global principle. (Constructions cachées en algèbre abstraite: Le principe local-global.) Zbl 1061.13007 Lombardi, Henri; Quitté, Claude 19 2003 Numerical univariate polynomial GCD. Zbl 0856.65006 Emiris, Ioannis Z.; Galligo, André; Lombardi, Henri 18 1996 An elementary characterization of Krull dimension. Zbl 1161.54303 Coquand, Thierry; Lombardi, Henri; Roy, Marie-Françoise 17 2005 Dynamical algebraic structures, pointfree topological spaces and Hilbert’s program. (Structures algébriques dynamiques, espaces topologiques sans points et programme de Hilbert). Zbl 1077.03039 Lombardi, Henri 15 2006 The Gröbner ring conjecture in one variable. Zbl 1242.13012 Lombardi, Henri; Schuster, Peter; Yengui, Ihsen 15 2012 Hidden constructions in abstract algebra. I: Integral dependance. Zbl 1099.13503 Lombardi, Henri 15 2002 Heitmann dimension of distributive lattices and commutative rings. (Dimension de Heitmann des treillis distributifs et des anneaux commutatifs.) Zbl 1158.13308 Coquand, Thierry; Lombardi, Henri; Quitté, Claude 12 2006 An elementary recursive bound for effective Positivstellensatz and Hilbert’s 17th problem. Zbl 1465.14001 Lombardi, Henri; Perrucci, Daniel; Roy, Marie-Françoise 12 2020 Constructive rereading of Artin-Schreier theory. (Relecture constructive de la théorie d’Artin-Schreier.) Zbl 0945.03094 Lombardi, Henri 12 1998 Lattice-ordered groups generated by an ordered group and regular systems of ideals. Zbl 1496.06018 Coquand, Thierry; Lombardi, Henri; Neuwirth, Stefan 11 2019 Generalized Budan–Fourier theorem and virtual roots. Zbl 1106.12001 Coste, Michel; Lajous-Loaeza, Tomás; Lombardi, Henri; Roy, Marie-Françoise 11 2005 A continuous and rational solution to Hilbert’s 17th problem and several cases of the Positivstellensatz. Zbl 0804.14001 Delzell, C. N.; González-Vega, Laureano; Lombardi, H. 10 1993 Generalizing Cramer’s rule: solving uniformly linear systems of equations. Zbl 1097.15006 Diaz-Toca, Gema M.; Gonzalez-Vega, Laureano; Lombardi, Henri 10 2005 Constructive content of a local-global principle with an application to the structure of a finitely generated projective module. (Le contenu constructif d’un principe local-global avec une application à la structure d’un module projectif de type fini.) Zbl 1221.13016 Lombardi, H. 9 1997 A bound on the degrees for the effective real Nullstellensatz. (Une borne sur les degrés pour le théorème des zeros reel effectif.) Zbl 0782.14001 Lombardi, Henri 9 1992 Constructive Krull dimension. I: Integral extensions. Zbl 1172.13007 Coquand, Thierry; Ducos, Lionel; Lombardi, Henri; Quitté, Claude 8 2009 Real numbers, continued fractions and complexity classes. Zbl 0715.03026 Labhalla, Salah; Lombardi, Henri 8 1990 Suslin’s algorithms for reduction of unimodular rows. Zbl 1120.13034 Lombardi, Henri; Yengui, Ihsen 8 2005 Hidden constructions in abstract algebra. VI: The theorem of Maroscia and Brewer & Costa. Zbl 1142.13006 Lombardi, Henri; Quitté, Claude; Yengui, Ihsen 8 2008 Effective real Nullstellensatz and variants. Zbl 0748.14023 Lombardi, Henri 7 1991 A constructive comparison of the rings \(R(X)\) and \(R\langle X\rangle\) and application to the Lequain-Simis induction theorem. Zbl 1147.13012 Ellouz, Afef; Lombardi, Henri; Yengui, Ihsen 7 2008 Elementary constructive theory of ordered fields. Zbl 0732.12002 Lombardi, Henri; Roy, Marie-Françoise 7 1991 The projective spectrum as a distributive lattice. Zbl 1131.03035 Coquand, Thierry; Lombardi, Henri; Schuster, Peter 7 2007 The Berlekamp-Massey algorithm revisited. Zbl 1107.11311 Atti, Nadia Ben; Diaz-Toca, Gema M.; Lombardi, Henri 6 2006 Virtual roots of real polynomials. Zbl 0893.12002 Gonzalez-Vega, Laureano; Lombardi, Henri; Mahé, Louis 6 1998 Hidden constructions in abstract algebra. V: Pfister’s local-global principle and variants. (Constructions cachées en algèbre abstraite. V: Principe local-global de Pfister et variantes.) Zbl 1165.12300 Lombardi, H. 5 2003 Spectral schemes as ringed lattices. Zbl 1254.03114 Coquand, Thierry; Lombardi, Henri; Schuster, Peter 5 2009 Computing algorithms for the reduction of a Hermite algorithm with polynomial coefficients. (Algorithmes de calcul de la réduction de Hermite d’une matrice à coefficients polynomiaux.) Zbl 0872.68055 Labhalla, Salah; Lombardi, Henri; Marlin, Roger 5 1996 A nilregular element property. Zbl 1093.03035 Coquand, Thierry; Lombardi, Henri; Schuster, Peter 5 2005 Specialization of the Sturm sequence. (Spécialisation de la suite de Sturm.) Zbl 0999.12502 González-Vega, Laureano; Lombardi, Henri; Recio, Thomas; Roy, Marie-Françoise 5 1994 A short proof for the Krull dimension of a polynomial ring. Zbl 1105.13301 Coquand, Thierry; Lombardi, Henri 5 2005 Projective modules over polynomial rings: a constructive approach. Zbl 1169.13003 Barhoumi, S.; Lombardi, H.; Yengui, I. 4 2009 Matrix methods. An introduction to algebraic complexity. (Méthodes matricielles. Introduction à la complexité algébrique.) Zbl 1087.65041 Abdeljaoued, Jounaïdi; Lombardi, Henri 4 2004 Hidden constructions in abstract algebra. IV: The solution of Hilbert’s 17th problem by Artin-Schreier theory. (Constructions cachées en algèbre abstraite: IV. La solution du 17ème problème de Hilbert par la théorie d’Artin-Schreier.) Zbl 1159.12306 Lombardi, H. 4 2002 An algorithm for computing the syzygies on \(V[X]\) when \(V\) is a valuation domain. (Un algorithme pour le calcul des syzygies sur \(V[X]\) dans le cas où \(V\) est un domaine de valuation.) Zbl 1312.13019 Lombardi, Henri; Quitté, Claude; Yengui, Ihsen 4 2014 The syzygy theorem for Bézout rings. Zbl 1439.13033 Gamanda, Maroua; Lombardi, Henri; Neuwirth, Stefan; Yengui, Ihsen 4 2020 Dynamic computations inside the algebraic closure of a valued field. Zbl 1060.12005 Kuhlmann, Franz-Viktor; Lombardi, Henri; Perdry, Hervé 3 2003 Rational presented metric spaces and complexity, the case of the space of real functions uniformly continuous on a compact interval. (Espaces métriques rationnellement présentés et complexité, le cas de l’espace des fonctions réelles uniformément continues sur un intervalle compact.) Zbl 0952.68068 Labhalla, S.; Lombardi, H.; Moutai, E. 3 2001 Effective real nullstellensatz and variants. (Théorème des zéros réel effectif et variantes.) Zbl 0787.14035 Lombardi, Henri 3 1989 Smooth parametrizations for several cases of the Positivstellensatz. Zbl 0892.14001 Gonzalez-Vega, Laureano; Lombardi, Henri 3 1997 The Positivstellensatz and small deduction rules for systems of inequalities. Zbl 0877.14001 Lombardi, Henri; Mnev, Nicolai; Roy, Marie-Françoise 3 1996 Revisiting Zariski main theorem from a constructive point of view. Zbl 1391.13049 Alonso, M. E.; Coquand, T.; Lombardi, H. 3 2014 A real Nullstellensatz and Positivstellensatz for the semipolynomials over an ordered field. Zbl 0826.12004 González-Vega, Laureano; Lombardi, Henri 3 1993 Finite type projective modules, crossed linear maps and generalized inverses. (Modules projectifs de type fini, applications linéaires croisées et inverses généralisés). Zbl 1104.15006 Diaz-Toca, Gema M.; Gonzalez-Vega, Laureano; Lombardi, Henri; Quitté, Claude 2 2006 Constructive study of problems of topology for the irrational reals. (Étude constructive de problèmes de topologie pour les réels irrationnels.) Zbl 0923.03072 Khalouani, Mohamed; Labhalla, Salah; Lombardi, Henri 2 1999 Local Bézout theorem. Zbl 1200.13051 Alonso, M. Emilia; Lombardi, Henri 2 2010 Continuity properties for flat families of polynomials. I: Continuous parametrizations. Zbl 1027.13014 Galligo, André; Gonzalez-Vega, Laureano; Lombardi, Henri 2 2003 Comparison of Picard groups in dimension 1. Zbl 1142.13007 Lombardi, Henri; Quitté, Claude 2 2008 Elementary constructive theory of Henselian local rings. Zbl 1143.13027 Alonso, María E.; Lombardi, Henri; Perdry, Hervé 2 2008 Spectral spaces versus distributive lattices: a dictionary. Zbl 1440.03060 Lombardi, Henri 2 2020 An algorithm for the Traverso-Swan theorem on seminormal rings. Zbl 1153.13019 Barhoumi, Sami; Lombardi, Henri 2 2008 Generalized Positivstellensatz for valued fields. (Une généralisation du Positivstellensatz pour les corps valués algébriquement clos.) Zbl 0993.12005 Lombardi, Henri 2 2000 The Buchberger algorithm as a tool for ideal theory of polynomial rings in constructive mathematics. Zbl 0926.13016 Lombardi, Henri; Perdry, Hervé 2 1998 Modules over commutative rings. Course and exercises. (Modules sur les anneaux commutatifs. Cours et exercices.) Zbl 1305.13001 Díaz-Toca, Gema-Maria; Lombardi, Henri; Quitté, Claude 2 2014 Dynamic Galois theory. Zbl 1237.12002 Diaz-Toca, G. M.; Lombardi, H. 2 2010 A Prüfer ring. (Un anneau de Prüfer.) Zbl 1439.13046 Lombardi, H. 2 2010 Nullstellensatz réel effectif et variantes. (Effective real Nullstellensatz and variations). Zbl 0719.14035 Lombardi, Henri 1 1990 Universal decomposition algebra. (L’algèbre de décomposition universelle.) Zbl 1190.12007 Diaz-Toca, Gema M.; Lombardi, Henri; Quitté, Claude 1 2006 Rings with divisors and Krull rings (a constructive approach). (Anneaux à diviseurs et anneaux de Krull (une approche constructive).) Zbl 1343.13019 Coquand, T.; Lombardi, H. 1 2016 Représentations des nombres réels par développements en base entière et complexité. (Representations of real numbers by expansions on integer basis and complexity). Zbl 0728.03032 Labhalla, Salah; Lombardi, Henri 1 1991 A note on the axiomatisation of real numbers. Zbl 1172.03030 Coquand, Thierry; Lombardi, L. Henri 1 2008 Valuative lattices and spectra. Zbl 1530.13009 Lombardi, Henri; Mahboubi, Assia 1 2023 Commutative algebra. Constructive methods. Finite type projective modules. Course and exercises. 2nd revised edition. (Algèbre commutative. Méthodes constructives. Modules projectifs de type fini. Cours et exercices.) Zbl 1545.13001 Lombardi, Henri; Quitté, Claude 1 2021 Deciding in HFS-theory via linear integer programming. Zbl 0790.90052 Hibti, M.; Lombardi, H.; Legeard, B. 1 1993 Seminormal rings (following Thierry Coquand). Zbl 1136.13004 Lombardi, Henri; Quitté, Claude 1 2008 Flatness, localization and Prüfer rings: a constructive approach. (Platitude, localisation et anneaux de Prüfer: une approche constructive.) Zbl 1095.13532 Lombardi, H. 1 2002 A decision procedure for a satisfiability problem in a hereditarily finite set-theoretical universe. (Une procédure de décision pour un problème de satisfiabilité dans un univers ensembliste héréditairement fini.) Zbl 0889.68062 Hibti, M.; Legeard, B.; Lombardi, H. 1 1997 Construction of the Henselization of a valued field. (Construction du hensélisé d’un corps valué.) Zbl 0966.12004 Kuhlmann, F.-V.; Lombardi, Henri 1 2000 Elementary algebra in polynimial time. (Algèbre élémentaire en temps polynômial.) Zbl 0825.12003 Lombardi, H. 1 1989 Homographic transformation applied to a finite or infinite continued fraction expansion. (Transformation homographique appliquée à un développement en fraction continue fini ou infini.) Zbl 0847.11005 Labhalla, Salah; Lombardi, Henri 1 1995 Local Bézout theorem for Henselian rings. Zbl 1390.13075 Alonso, M. Emilia; Lombardi, Henri 1 2017 Curves and coherent Prüfer rings. Zbl 1203.13020 Coquand, Thierry; Lombardi, Henri; Quitté, Claude 1 2010 Geometric theories for the algebra of real numbers. (Théories géométriques pour l’algèbre des nombres réels.) Zbl 1393.13048 Lombardi, Henri; Mahboubi, Assia 1 2017 Valuative lattices and spectra. Zbl 1530.13009 Lombardi, Henri; Mahboubi, Assia 1 2023 Commutative algebra. Constructive methods. Finite type projective modules. Course and exercises. 2nd revised edition. (Algèbre commutative. Méthodes constructives. Modules projectifs de type fini. Cours et exercices.) Zbl 1545.13001 Lombardi, Henri; Quitté, Claude 1 2021 An elementary recursive bound for effective Positivstellensatz and Hilbert’s 17th problem. Zbl 1465.14001 Lombardi, Henri; Perrucci, Daniel; Roy, Marie-Françoise 12 2020 The syzygy theorem for Bézout rings. Zbl 1439.13033 Gamanda, Maroua; Lombardi, Henri; Neuwirth, Stefan; Yengui, Ihsen 4 2020 Spectral spaces versus distributive lattices: a dictionary. Zbl 1440.03060 Lombardi, Henri 2 2020 Lattice-ordered groups generated by an ordered group and regular systems of ideals. Zbl 1496.06018 Coquand, Thierry; Lombardi, Henri; Neuwirth, Stefan 11 2019 Local Bézout theorem for Henselian rings. Zbl 1390.13075 Alonso, M. Emilia; Lombardi, Henri 1 2017 Geometric theories for the algebra of real numbers. (Théories géométriques pour l’algèbre des nombres réels.) Zbl 1393.13048 Lombardi, Henri; Mahboubi, Assia 1 2017 Rings with divisors and Krull rings (a constructive approach). (Anneaux à diviseurs et anneaux de Krull (une approche constructive).) Zbl 1343.13019 Coquand, T.; Lombardi, H. 1 2016 Commutative algebra: constructive methods. Finite projective modules. Translated from the French by Tania K. Roblot. Zbl 1327.13001 Lombardi, Henri; Quitté, Claude 52 2015 An algorithm for computing the syzygies on \(V[X]\) when \(V\) is a valuation domain. (Un algorithme pour le calcul des syzygies sur \(V[X]\) dans le cas où \(V\) est un domaine de valuation.) Zbl 1312.13019 Lombardi, Henri; Quitté, Claude; Yengui, Ihsen 4 2014 Revisiting Zariski main theorem from a constructive point of view. Zbl 1391.13049 Alonso, M. E.; Coquand, T.; Lombardi, H. 3 2014 Modules over commutative rings. Course and exercises. (Modules sur les anneaux commutatifs. Cours et exercices.) Zbl 1305.13001 Díaz-Toca, Gema-Maria; Lombardi, Henri; Quitté, Claude 2 2014 The Gröbner ring conjecture in one variable. Zbl 1242.13012 Lombardi, Henri; Schuster, Peter; Yengui, Ihsen 15 2012 Commutative algebra. Constructive methods. Finite type projective modules. Course and exercises. (Algèbre commutative. Méthodes constructives. Modules projectifs de type fini. Cours et exercices.) Zbl 1242.13002 Lombardi, Henri; Quitté, Claude 27 2011 Local Bézout theorem. Zbl 1200.13051 Alonso, M. Emilia; Lombardi, Henri 2 2010 Dynamic Galois theory. Zbl 1237.12002 Diaz-Toca, G. M.; Lombardi, H. 2 2010 A Prüfer ring. (Un anneau de Prüfer.) Zbl 1439.13046 Lombardi, H. 2 2010 Curves and coherent Prüfer rings. Zbl 1203.13020 Coquand, Thierry; Lombardi, Henri; Quitté, Claude 1 2010 Constructive Krull dimension. I: Integral extensions. Zbl 1172.13007 Coquand, Thierry; Ducos, Lionel; Lombardi, Henri; Quitté, Claude 8 2009 Spectral schemes as ringed lattices. Zbl 1254.03114 Coquand, Thierry; Lombardi, Henri; Schuster, Peter 5 2009 Projective modules over polynomial rings: a constructive approach. Zbl 1169.13003 Barhoumi, S.; Lombardi, H.; Yengui, I. 4 2009 Hidden constructions in abstract algebra. VI: The theorem of Maroscia and Brewer & Costa. Zbl 1142.13006 Lombardi, Henri; Quitté, Claude; Yengui, Ihsen 8 2008 A constructive comparison of the rings \(R(X)\) and \(R\langle X\rangle\) and application to the Lequain-Simis induction theorem. Zbl 1147.13012 Ellouz, Afef; Lombardi, Henri; Yengui, Ihsen 7 2008 Comparison of Picard groups in dimension 1. Zbl 1142.13007 Lombardi, Henri; Quitté, Claude 2 2008 Elementary constructive theory of Henselian local rings. Zbl 1143.13027 Alonso, María E.; Lombardi, Henri; Perdry, Hervé 2 2008 An algorithm for the Traverso-Swan theorem on seminormal rings. Zbl 1153.13019 Barhoumi, Sami; Lombardi, Henri 2 2008 A note on the axiomatisation of real numbers. Zbl 1172.03030 Coquand, Thierry; Lombardi, L. Henri 1 2008 Seminormal rings (following Thierry Coquand). Zbl 1136.13004 Lombardi, Henri; Quitté, Claude 1 2008 The projective spectrum as a distributive lattice. Zbl 1131.03035 Coquand, Thierry; Lombardi, Henri; Schuster, Peter 7 2007 A logical approach to abstract algebra. Zbl 1118.03059 Coquand, Thierry; Lombardi, Henri 28 2006 Dynamical algebraic structures, pointfree topological spaces and Hilbert’s program. (Structures algébriques dynamiques, espaces topologiques sans points et programme de Hilbert). Zbl 1077.03039 Lombardi, Henri 15 2006 Heitmann dimension of distributive lattices and commutative rings. (Dimension de Heitmann des treillis distributifs et des anneaux commutatifs.) Zbl 1158.13308 Coquand, Thierry; Lombardi, Henri; Quitté, Claude 12 2006 The Berlekamp-Massey algorithm revisited. Zbl 1107.11311 Atti, Nadia Ben; Diaz-Toca, Gema M.; Lombardi, Henri 6 2006 Finite type projective modules, crossed linear maps and generalized inverses. (Modules projectifs de type fini, applications linéaires croisées et inverses généralisés). Zbl 1104.15006 Diaz-Toca, Gema M.; Gonzalez-Vega, Laureano; Lombardi, Henri; Quitté, Claude 2 2006 Universal decomposition algebra. (L’algèbre de décomposition universelle.) Zbl 1190.12007 Diaz-Toca, Gema M.; Lombardi, Henri; Quitté, Claude 1 2006 An elementary characterization of Krull dimension. Zbl 1161.54303 Coquand, Thierry; Lombardi, Henri; Roy, Marie-Françoise 17 2005 Generalized Budan–Fourier theorem and virtual roots. Zbl 1106.12001 Coste, Michel; Lajous-Loaeza, Tomás; Lombardi, Henri; Roy, Marie-Françoise 11 2005 Generalizing Cramer’s rule: solving uniformly linear systems of equations. Zbl 1097.15006 Diaz-Toca, Gema M.; Gonzalez-Vega, Laureano; Lombardi, Henri 10 2005 Suslin’s algorithms for reduction of unimodular rows. Zbl 1120.13034 Lombardi, Henri; Yengui, Ihsen 8 2005 A nilregular element property. Zbl 1093.03035 Coquand, Thierry; Lombardi, Henri; Schuster, Peter 5 2005 A short proof for the Krull dimension of a polynomial ring. Zbl 1105.13301 Coquand, Thierry; Lombardi, Henri 5 2005 Generating non-Noetherian modules constructively. Zbl 1059.13006 Coquand, Thierry; Lombardi, Henri; Quitté, Claude 24 2004 Algorithmic theory of arithmetic rings, Prüfer rings and Dedekind rings. (Théorie algorithmique des anneaux arithmétiques, des anneaux de Prüfer et des anneaux de Dedekind.). Zbl 1093.13015 Ducos, L.; Lombardi, H.; Quitté, C.; Salou, M. 20 2004 Matrix methods. An introduction to algebraic complexity. (Méthodes matricielles. Introduction à la complexité algébrique.) Zbl 1087.65041 Abdeljaoued, Jounaïdi; Lombardi, Henri 4 2004 Hidden constructions in abstract algebra: Krull dimension of distributive lattice and commutative rings. Zbl 1096.13507 Coquand, Thierry; Lombardi, Henri 41 2003 Hidden constructions in abstract algebra: The local-global principle. (Constructions cachées en algèbre abstraite: Le principe local-global.) Zbl 1061.13007 Lombardi, Henri; Quitté, Claude 19 2003 Hidden constructions in abstract algebra. V: Pfister’s local-global principle and variants. (Constructions cachées en algèbre abstraite. V: Principe local-global de Pfister et variantes.) Zbl 1165.12300 Lombardi, H. 5 2003 Dynamic computations inside the algebraic closure of a valued field. Zbl 1060.12005 Kuhlmann, Franz-Viktor; Lombardi, Henri; Perdry, Hervé 3 2003 Continuity properties for flat families of polynomials. I: Continuous parametrizations. Zbl 1027.13014 Galligo, André; Gonzalez-Vega, Laureano; Lombardi, Henri 2 2003 Krull dimension, Nullstellensätze and dynamical evaluation. (Dimension de Krull, Nullstellensätze et évaluation dynamique.) Zbl 1095.13517 Lombardi, Henri 25 2002 Hidden constructions in abstract algebra. I: Integral dependance. Zbl 1099.13503 Lombardi, Henri 15 2002 Hidden constructions in abstract algebra. IV: The solution of Hilbert’s 17th problem by Artin-Schreier theory. (Constructions cachées en algèbre abstraite: IV. La solution du 17ème problème de Hilbert par la théorie d’Artin-Schreier.) Zbl 1159.12306 Lombardi, H. 4 2002 Flatness, localization and Prüfer rings: a constructive approach. (Platitude, localisation et anneaux de Prüfer: une approche constructive.) Zbl 1095.13532 Lombardi, H. 1 2002 Dynamical method in algebra: Effective Nullstellensätze. Zbl 0992.03076 Coste, Michel; Lombardi, Henri; Roy, Marie-Françoise 57 2001 Rational presented metric spaces and complexity, the case of the space of real functions uniformly continuous on a compact interval. (Espaces métriques rationnellement présentés et complexité, le cas de l’espace des fonctions réelles uniformément continues sur un intervalle compact.) Zbl 0952.68068 Labhalla, S.; Lombardi, H.; Moutai, E. 3 2001 New structure theorem for subresultants. Zbl 0973.12007 Lombardi, Henri; Roy, Marie-Françoise; El Din, Mohab Safey 21 2000 Generalized Positivstellensatz for valued fields. (Une généralisation du Positivstellensatz pour les corps valués algébriquement clos.) Zbl 0993.12005 Lombardi, Henri 2 2000 Construction of the Henselization of a valued field. (Construction du hensélisé d’un corps valué.) Zbl 0966.12004 Kuhlmann, F.-V.; Lombardi, Henri 1 2000 Constructive study of problems of topology for the irrational reals. (Étude constructive de problèmes de topologie pour les réels irrationnels.) Zbl 0923.03072 Khalouani, Mohamed; Labhalla, Salah; Lombardi, Henri 2 1999 Sturm-Habicht sequences, determinants and real roots of univariate polynomials. Zbl 0900.12002 González-Vega, L.; Recio, T.; Lombardi, H.; Roy, M.-F. 26 1998 Constructive rereading of Artin-Schreier theory. (Relecture constructive de la théorie d’Artin-Schreier.) Zbl 0945.03094 Lombardi, Henri 12 1998 Virtual roots of real polynomials. Zbl 0893.12002 Gonzalez-Vega, Laureano; Lombardi, Henri; Mahé, Louis 6 1998 The Buchberger algorithm as a tool for ideal theory of polynomial rings in constructive mathematics. Zbl 0926.13016 Lombardi, Henri; Perdry, Hervé 2 1998 Certified approximate univariate GCDs. Zbl 0891.65015 Emiris, Ioannis Z.; Galligo, André; Lombardi, Henri 56 1997 Constructive content of a local-global principle with an application to the structure of a finitely generated projective module. (Le contenu constructif d’un principe local-global avec une application à la structure d’un module projectif de type fini.) Zbl 1221.13016 Lombardi, H. 9 1997 Smooth parametrizations for several cases of the Positivstellensatz. Zbl 0892.14001 Gonzalez-Vega, Laureano; Lombardi, Henri 3 1997 A decision procedure for a satisfiability problem in a hereditarily finite set-theoretical universe. (Une procédure de décision pour un problème de satisfiabilité dans un univers ensembliste héréditairement fini.) Zbl 0889.68062 Hibti, M.; Legeard, B.; Lombardi, H. 1 1997 Numerical univariate polynomial GCD. Zbl 0856.65006 Emiris, Ioannis Z.; Galligo, André; Lombardi, Henri 18 1996 Computing algorithms for the reduction of a Hermite algorithm with polynomial coefficients. (Algorithmes de calcul de la réduction de Hermite d’une matrice à coefficients polynomiaux.) Zbl 0872.68055 Labhalla, Salah; Lombardi, Henri; Marlin, Roger 5 1996 The Positivstellensatz and small deduction rules for systems of inequalities. Zbl 0877.14001 Lombardi, Henri; Mnev, Nicolai; Roy, Marie-Françoise 3 1996 Homographic transformation applied to a finite or infinite continued fraction expansion. (Transformation homographique appliquée à un développement en fraction continue fini ou infini.) Zbl 0847.11005 Labhalla, Salah; Lombardi, Henri 1 1995 Specialization of the Sturm sequence. (Spécialisation de la suite de Sturm.) Zbl 0999.12502 González-Vega, Laureano; Lombardi, Henri; Recio, Thomas; Roy, Marie-Françoise 5 1994 A continuous and rational solution to Hilbert’s 17th problem and several cases of the Positivstellensatz. Zbl 0804.14001 Delzell, C. N.; González-Vega, Laureano; Lombardi, H. 10 1993 A real Nullstellensatz and Positivstellensatz for the semipolynomials over an ordered field. Zbl 0826.12004 González-Vega, Laureano; Lombardi, Henri 3 1993 Deciding in HFS-theory via linear integer programming. Zbl 0790.90052 Hibti, M.; Lombardi, H.; Legeard, B. 1 1993 A bound on the degrees for the effective real Nullstellensatz. (Une borne sur les degrés pour le théorème des zeros reel effectif.) Zbl 0782.14001 Lombardi, Henri 9 1992 Effective real Nullstellensatz and variants. Zbl 0748.14023 Lombardi, Henri 7 1991 Elementary constructive theory of ordered fields. Zbl 0732.12002 Lombardi, Henri; Roy, Marie-Françoise 7 1991 Représentations des nombres réels par développements en base entière et complexité. (Representations of real numbers by expansions on integer basis and complexity). Zbl 0728.03032 Labhalla, Salah; Lombardi, Henri 1 1991 Spécialisation de la suite de Sturm et sous-résultants. I. (Specialization of the Sturm sequence and subresultants. I). Zbl 0732.68059 González-Vega, L.; Lombardi, H.; Recio, T.; Roy, M.-F. 24 1990 Real numbers, continued fractions and complexity classes. Zbl 0715.03026 Labhalla, Salah; Lombardi, Henri 8 1990 Nullstellensatz réel effectif et variantes. (Effective real Nullstellensatz and variations). Zbl 0719.14035 Lombardi, Henri 1 1990 Effective real nullstellensatz and variants. (Théorème des zéros réel effectif et variantes.) Zbl 0787.14035 Lombardi, Henri 3 1989 Elementary algebra in polynimial time. (Algèbre élémentaire en temps polynômial.) Zbl 0825.12003 Lombardi, H. 1 1989 all cited Publications top 5 cited Publications all top 5 Cited by 370 Authors 46 Lombardi, Henri 30 Yengui, Ihsen 21 Schuster, Peter Michael 17 Coquand, Thierry 15 Gonzalez-Vega, Laureano 15 Wessel, Daniel 14 Díaz-Toca, Gema María 10 Ducos, Lionel 9 Galligo, André 9 Rinaldi, Davide 9 Roy, Marie-Françoise 8 Quitté, Claude 6 Anai, Hirokazu 6 Neuwirth, Stefan 5 El Kahoui, M’hammed 5 Nagasaka, Kosaku 5 Pérez-Díaz, Sonia 5 Sendra, Juan Rafael 5 Sendra, Juana 4 Barhoumi, Sami 4 Christou, Dimitrios 4 Hara, Shinji 4 Kaltofen, Erich L. 4 Kanno, Masaaki 4 Karcanias, Nicos 4 Labhalla, Salah 4 Mitrouli, Marilena 4 Monagan, Michael B. 4 Mourrain, Bernard 4 Sagraloff, Michael 4 Terui, Akira 4 Winkler, Joab R. 4 Yokoyama, Kazuhiro 4 Zeng, Zhonggang 4 Zhi, Lihong 3 Alonso García, María Emilia 3 Amidou, Morou 3 Ben Amor, Faten 3 Giesbrecht, Mark W. 3 Guyot, Luc 3 Hong, Hoon 3 Kerber, Michael 3 Li, Dongmei 3 Liu, Jinwang 3 Misselbeck-Wessel, Daniel 3 Pan, Victor Yakovlevich 3 Perdry, Hervé 3 Perrucci, Daniel 3 Safey El Din, Mohab 3 Schost, Éric 3 Storjohann, Arne 3 Szántó, Ágnes 3 Yakoubsohn, Jean-Claude 3 Yang, Zhengfeng 2 Abdeljaoued, Jounaïdi 2 Baldi, Lorenzo 2 Bembé, Daniel 2 Blechschmidt, Ingo 2 Busé, Laurent 2 Buss, Samuel R. 2 Caravantes, Jorge 2 Chèze, Guillaume 2 Coste, Michel 2 D’Andrea, Carlos 2 Dube, Themba Andrew 2 Elkadi, Mohamed 2 Fioravanti, Mario A. 2 Gallego, Claudia 2 Gamanda, Maroua 2 Georgiev, Ivan 2 Gouveia, Joao 2 Grigor’ev, Dmitriĭ Yur’evich 2 Hu, Jiaxiong 2 Huang, Chengchao 2 Iemhoff, Rosalie 2 Jeronimo, Gabriela 2 Jinadu, Ayoola 2 Kawamura, Akitoshi 2 Kemper, Gregor 2 Kohlenbach, Ulrich Wilhelm 2 Kress, Jonathan M. 2 Krick, Teresa 2 Kristiansen, Lars 2 Lao, Xin 2 Lecerf, Grégoire 2 Lezama, Oswaldo 2 Li, Bingyu 2 Li, Jing-Cao 2 Li, Zhibin 2 Magron, Victor 2 Mahboubi, Assia 2 May, John P. 2 Mnif, Abdessalem 2 Monceur, Samiha 2 Moreno Maza, Marc 2 Necula, Ioana 2 Quadrat, Alban 2 Rathjen, Michael 2 Recio, Tomas 2 Robertz, Daniel ...and 270 more Authors all top 5 Cited in 96 Serials 43 Journal of Symbolic Computation 38 Journal of Algebra 18 Journal of Pure and Applied Algebra 18 Theoretical Computer Science 12 Annals of Pure and Applied Logic 9 Linear Algebra and its Applications 8 Journal of Computational and Applied Mathematics 6 Computer Aided Geometric Design 5 Communications in Algebra 5 Applied Mathematics and Computation 5 Applicable Algebra in Engineering, Communication and Computing 4 Mathematische Zeitschrift 4 Journal of Complexity 4 The Bulletin of Symbolic Logic 4 Journal of Algebra and its Applications 3 Mathematics of Computation 3 Information and Computation 3 Mathematical Structures in Computer Science 3 RAIRO. Informatique Théorique et Applications 3 Mathematical Programming. Series A. Series B 3 Foundations of Computational Mathematics 3 Mathematics in Computer Science 3 Confluentes Mathematici 3 Computability 2 Computers & Mathematics with Applications 2 Linear and Multilinear Algebra 2 Algebra Universalis 2 Compositio Mathematica 2 The Journal of Symbolic Logic 2 Proceedings of the American Mathematical Society 2 Applied Numerical Mathematics 2 Computational Geometry 2 International Journal of Computer Mathematics 2 Mathematical Logic Quarterly (MLQ) 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Oberwolfach Reports 2 Journal of Commutative Algebra 1 Acta Mechanica 1 American Mathematical Monthly 1 Communications in Mathematical Physics 1 Discrete Mathematics 1 Information Processing Letters 1 Israel Journal of Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematische Semesterberichte 1 Rocky Mountain Journal of Mathematics 1 Archiv der Mathematik 1 Bulletin de la Société Mathématique de France 1 Calcolo 1 Collectanea Mathematica 1 Czechoslovak Mathematical Journal 1 Dissertationes Mathematicae 1 Fuzzy Sets and Systems 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Combinatorial Theory. Series A 1 Manuscripta Mathematica 1 Matematički Vesnik 1 Mathematische Nachrichten 1 Memoirs of the American Mathematical Society 1 Revista de la Unión Matemática Argentina 1 Ricerche di Matematica 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Systems & Control Letters 1 Acta Mathematica Hungarica 1 Acta Applicandae Mathematicae 1 Journal of Automated Reasoning 1 MCSS. Mathematics of Control, Signals, and Systems 1 Multidimensional Systems and Signal Processing 1 Real-Time Systems 1 Japan Journal of Industrial and Applied Mathematics 1 The Journal of Geometric Analysis 1 Numerical Algorithms 1 Archive for Mathematical Logic 1 Indagationes Mathematicae. New Series 1 Filomat 1 Bulletin des Sciences Mathématiques 1 Annals of Mathematics and Artificial Intelligence 1 The Journal of Fourier Analysis and Applications 1 Science in China. Series E 1 Soft Computing 1 Journal of Systems Science and Complexity 1 JP Journal of Algebra, Number Theory and Applications 1 Cahiers de Topologie et Géométrie Différentielle Catégoriques 1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 1 Hacettepe Journal of Mathematics and Statistics 1 Acta Mathematica Sinica. Chinese Series 1 Logical Methods in Computer Science 1 Applicable Analysis and Discrete Mathematics 1 São Paulo Journal of Mathematical Sciences 1 Armenian Journal of Mathematics 1 Science China. Mathematics 1 Journal of the Operations Research Society of China 1 Journal of Mathematics 1 Khayyam Journal of Mathematics 1 Actes des Rencontres du C.I.R.M. all top 5 Cited in 40 Fields 152 Commutative algebra (13-XX) 118 Computer science (68-XX) 98 Mathematical logic and foundations (03-XX) 75 Numerical analysis (65-XX) 73 Field theory and polynomials (12-XX) 72 Algebraic geometry (14-XX) 31 Order, lattices, ordered algebraic structures (06-XX) 26 Number theory (11-XX) 25 Linear and multilinear algebra; matrix theory (15-XX) 17 \(K\)-theory (19-XX) 12 Associative rings and algebras (16-XX) 11 Real functions (26-XX) 10 Operations research, mathematical programming (90-XX) 7 Category theory; homological algebra (18-XX) 6 General topology (54-XX) 6 Systems theory; control (93-XX) 5 Functions of a complex variable (30-XX) 4 Group theory and generalizations (20-XX) 4 Functional analysis (46-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Measure and integration (28-XX) 3 Ordinary differential equations (34-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Information and communication theory, circuits (94-XX) 2 Combinatorics (05-XX) 2 General algebraic systems (08-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Approximations and expansions (41-XX) 2 Mechanics of particles and systems (70-XX) 1 Topological groups, Lie groups (22-XX) 1 Special functions (33-XX) 1 Partial differential equations (35-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of deformable solids (74-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) Citations by Year