Edit Profile (opens in new tab) Trager, Barry M. Co-Author Distance Author ID: trager.barry-m Published as: Trager, Barry M.; Trager, B.; Trager, Barry; Trager, B. M. more...less Documents Indexed: 26 Publications since 1976, including 1 Additional arXiv Preprint Co-Authors: 22 Co-Authors with 22 Joint Publications 461 Co-Co-Authors all top 5 Co-Authors 4 single-authored 14 Gianni, Patrizia M. 7 Fortuna, Elisabetta 3 Davenport, James Harold 2 Corless, Robert Malcolm 1 Cormier, Olivier 1 El-Zein, Ali 1 Jenks, Richard Dimick 1 Kaltofen, Erich L. 1 Lastras-Montaño, Luis Alfonso 1 Lvov, Alexey 1 Paruthi, Viresh 1 Pestun, Vasily 1 Seppälä, Mika 1 Shadowen, Robert 1 Shinnar, Avraham 1 Silhol, Robert 1 Singer, Michael F. 1 Ulmer, Felix 1 Vajjha, Koundinya 1 Wang, Paul S. 1 Watt, Stephen Michael 1 Zacharias, Gail all top 5 Serials 8 Journal of Symbolic Computation 1 ACM Transactions on Mathematical Software 1 Journal of Pure and Applied Algebra 1 SIAM Journal on Computing 1 Applicable Algebra in Engineering, Communication and Computing 1 Formal Methods in System Design all top 5 Fields 13 Computer science (68-XX) 11 Commutative algebra (13-XX) 10 Field theory and polynomials (12-XX) 4 Number theory (11-XX) 4 Algebraic geometry (14-XX) 4 Real functions (26-XX) 4 Numerical analysis (65-XX) 2 Functions of a complex variable (30-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Operator theory (47-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 21 Publications have been cited 422 times in 392 Documents Cited by ▼ Year ▼ Gröbner bases and primary decomposition of polynomial ideals. Zbl 0667.13008 Gianni, Patrizia; Trager, Barry; Zacharias, Gail 176 1988 The singular value decomposition for polynomial systems. Zbl 0920.65034 Corless, Robert M.; Gianni, Patrizia M.; Trager, Barry M.; Watt, Stephen M. 61 1995 Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators. Zbl 0712.12001 Kaltofen, Erich; Trager, Barry M. 39 1990 Algebraic factoring and rational function integration. Zbl 0498.12005 Trager, Barry M. 35 1976 A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots. Zbl 0917.65048 Corless, Robert M.; Gianni, Patrizia M.; Trager, Barry M. 31 1997 Linear differential operators for polynomial equations. Zbl 1030.12002 Cormier, Olivier; Singer, Michael F.; Trager, Barry M.; Ulmer, Felix 12 2002 Riemann surfaces, plane algebraic curves and their period matrices. Zbl 0964.14047 Gianni, Patrizia; Seppälä, Mika; Silhol, Robert; Trager, Barry 10 1998 Square-free algorithms in positive characteristic. Zbl 0874.12009 Gianni, P.; Trager, B. 9 1996 On the parallel Risch algorithm. II. Zbl 0606.68032 Davenport, J. H.; Trager, B. M. 9 1985 Degree reduction under specialization. Zbl 0998.13014 Fortuna, Elisabetta; Gianni, Patrizia; Trager, Barry 8 2001 Factorization over finitely generated fields. Zbl 0481.68040 Davenport, James H.; Trager, Barry M. 5 1981 Integral closure of Noetherian rings. Zbl 0927.13012 Gianni, P.; Trager, B. 5 1997 Derivations and radicals of polynomial ideals over fields of arbitrary characteristic. Zbl 1059.13014 Fortuna, E.; Gianni, P.; Trager, B. 5 2002 Scratchpad’s view of algebra. II: A categorical view of factorization. Zbl 0921.13011 Davenport, J. H.; Gianni, P.; Trager, B. M. 4 1991 Irreducible decomposition of polynomial ideals. Zbl 1120.13017 Fortuna, E.; Gianni, P.; Trager, B. 3 2005 Integration of simple radical extensions. Zbl 0411.12020 Trager, Barry M. 3 1979 Generators of the ideal of an algebraic space curve. Zbl 1169.14024 Fortuna, E.; Gianni, P.; Trager, B. 2 2009 Integration of algebraic functions. Zbl 1511.26013 Trager, Barry M. 2 2022 New algorithms for polynomial square-free decomposition over the integers. Zbl 0415.10050 Wang, Paul S.; Trager, Barry M. 1 1979 Ideals of curves given by points. Zbl 1317.13062 Fortuna, E.; Gianni, P.; Trager, B. 1 2012 Verification of Galois field based circuits by formal reasoning based on computational algebraic geometry. Zbl 1303.94146 Lvov, Alexey; Lastras-Montaño, Luis A.; Trager, Barry; Paruthi, Viresh; Shadowen, Robert; El-Zein, Ali 1 2014 Integration of algebraic functions. Zbl 1511.26013 Trager, Barry M. 2 2022 Verification of Galois field based circuits by formal reasoning based on computational algebraic geometry. Zbl 1303.94146 Lvov, Alexey; Lastras-Montaño, Luis A.; Trager, Barry; Paruthi, Viresh; Shadowen, Robert; El-Zein, Ali 1 2014 Ideals of curves given by points. Zbl 1317.13062 Fortuna, E.; Gianni, P.; Trager, B. 1 2012 Generators of the ideal of an algebraic space curve. Zbl 1169.14024 Fortuna, E.; Gianni, P.; Trager, B. 2 2009 Irreducible decomposition of polynomial ideals. Zbl 1120.13017 Fortuna, E.; Gianni, P.; Trager, B. 3 2005 Linear differential operators for polynomial equations. Zbl 1030.12002 Cormier, Olivier; Singer, Michael F.; Trager, Barry M.; Ulmer, Felix 12 2002 Derivations and radicals of polynomial ideals over fields of arbitrary characteristic. Zbl 1059.13014 Fortuna, E.; Gianni, P.; Trager, B. 5 2002 Degree reduction under specialization. Zbl 0998.13014 Fortuna, Elisabetta; Gianni, Patrizia; Trager, Barry 8 2001 Riemann surfaces, plane algebraic curves and their period matrices. Zbl 0964.14047 Gianni, Patrizia; Seppälä, Mika; Silhol, Robert; Trager, Barry 10 1998 A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots. Zbl 0917.65048 Corless, Robert M.; Gianni, Patrizia M.; Trager, Barry M. 31 1997 Integral closure of Noetherian rings. Zbl 0927.13012 Gianni, P.; Trager, B. 5 1997 Square-free algorithms in positive characteristic. Zbl 0874.12009 Gianni, P.; Trager, B. 9 1996 The singular value decomposition for polynomial systems. Zbl 0920.65034 Corless, Robert M.; Gianni, Patrizia M.; Trager, Barry M.; Watt, Stephen M. 61 1995 Scratchpad’s view of algebra. II: A categorical view of factorization. Zbl 0921.13011 Davenport, J. H.; Gianni, P.; Trager, B. M. 4 1991 Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators. Zbl 0712.12001 Kaltofen, Erich; Trager, Barry M. 39 1990 Gröbner bases and primary decomposition of polynomial ideals. Zbl 0667.13008 Gianni, Patrizia; Trager, Barry; Zacharias, Gail 176 1988 On the parallel Risch algorithm. II. Zbl 0606.68032 Davenport, J. H.; Trager, B. M. 9 1985 Factorization over finitely generated fields. Zbl 0481.68040 Davenport, James H.; Trager, Barry M. 5 1981 Integration of simple radical extensions. Zbl 0411.12020 Trager, Barry M. 3 1979 New algorithms for polynomial square-free decomposition over the integers. Zbl 0415.10050 Wang, Paul S.; Trager, Barry M. 1 1979 Algebraic factoring and rational function integration. Zbl 0498.12005 Trager, Barry M. 35 1976 all cited Publications top 5 cited Publications all top 5 Cited by 528 Authors 29 Romanovskiĭ, Valeriĭ Georgievich 15 Giné, Jaume 11 Winkler, Joab R. 10 Mourrain, Bernard 8 Zhi, Lihong 7 Kaltofen, Erich L. 7 Pan, Victor Yakovlevich 7 Sendra, Juan Rafael 6 Sendra, Juana 6 Valls Anglés, Cláudia 5 Bourne, Martin 5 Chèze, Guillaume 5 Ferčec, Brigita 5 Fernandes, Wilker 5 Han, Maoan 5 Nie, Jiawang 5 Oliveira, Regilene D. S. 5 Swanson, Irena 5 Szántó, Ágnes 5 Wang, Dongming 5 Zhang, Weinian 4 Bronstein, Manuel Eric 4 Galligo, André 4 Lecerf, Grégoire 4 Lee, Wen-shin 4 Noro, Masayuki 4 Pérez-Díaz, Sonia 4 Pfister, Gerhard 4 Poteaux, Adrien 4 Su, Yi 4 Trager, Barry M. 4 Yokoyama, Kazuhiro 4 Yu, Zhiheng 3 Aschenbrenner, Matthias 3 Bostan, Alin 3 De Moor, Bart L. R. 3 Dibitetto, Giuseppe 3 Dukarić, Maša 3 Fortuna, Elisabetta 3 Gao, Xiaoshan 3 Gianni, Patrizia M. 3 Giesbrecht, Mark W. 3 Hasan, Madina 3 Hauenstein, Jonathan D. 3 Hidalgo, Rubén Antonio 3 Karcanias, Nicos 3 Lao, Xin 3 Levandovskyy, Viktor 3 Llibre, Jaume 3 Markovsky, Ivan 3 Martínez-Moro, Edgar 3 Mitrouli, Marilena 3 Monagan, Michael B. 3 Montes, Antonio 3 Mora, Teo 3 Mou, Chenqi 3 Rueda, Sonia L. 3 Safey El Din, Mohab 3 Sasaki, Tateaki 3 Singer, Michael F. 3 Sinhababu, Amit 3 Tajima, Shinichi 3 Telen, Simon 3 Terui, Akira 3 Van Barel, Marc 2 Algaba, Antonio 2 Apel, Joachim 2 Arvind, Vikraman 2 Aybar, Orhan Ozgur 2 Batselier, Kim 2 Beckermann, Bernhard 2 Bousquet-Mélou, Mireille 2 Busé, Laurent 2 Cangelmi, Leonardo 2 Chen, Shaoshi 2 Chen, Tian 2 Cheng, Jinsan 2 Chou, Shangching 2 Christou, Dimitrios 2 Corless, Robert Malcolm 2 Davenport, James Harold 2 De Lathauwer, Lieven 2 Deconinck, Bernard 2 Dreesen, Philippe 2 Eder, Christian 2 Edneral, Victor F. 2 Eisenbud, David 2 Emiris, Ioannis Z. 2 Feng, Ruyong 2 Feng, Yong 2 Frauendiener, Jörg 2 Gao, Shuhong 2 García, Cristóbal 2 Gray, James A. 2 Greuel, Gert-Martin 2 Guerrieri, Anna 2 Guglielmi, Nicola 2 Gutierrez, Jaime 2 Hu, Zhaoping 2 Huang, Qiaolong ...and 428 more Authors all top 5 Cited in 107 Serials 86 Journal of Symbolic Computation 20 Theoretical Computer Science 17 Applicable Algebra in Engineering, Communication and Computing 15 Mathematics of Computation 12 Journal of Computational and Applied Mathematics 11 Journal of Pure and Applied Algebra 10 Linear Algebra and its Applications 8 Mathematics in Computer Science 7 Applied Mathematics and Computation 6 Computers & Mathematics with Applications 6 Journal of Algebra 5 Journal of Mathematical Analysis and Applications 5 Computer Aided Geometric Design 5 Journal of Complexity 5 Computational Complexity 5 Journal of High Energy Physics 4 Communications in Algebra 4 Programming and Computer Software 4 Qualitative Theory of Dynamical Systems 4 Journal of Algebra and its Applications 3 Computer Physics Communications 3 Journal of Differential Equations 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Transactions of the American Mathematical Society 3 Physica D 3 Applied Numerical Mathematics 3 Discrete & Computational Geometry 3 Information and Computation 3 SIAM Journal on Matrix Analysis and Applications 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Foundations of Computational Mathematics 2 Annales de l’Institut Fourier 2 Bulletin of the London Mathematical Society 2 Advances in Applied Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Revista Matemática Iberoamericana 2 Journal of the American Mathematical Society 2 Science in China. Series A 2 Numerical Algorithms 2 Computational Optimization and Applications 2 Nonlinear Dynamics 2 Journal of Systems Science and Complexity 2 Central European Journal of Mathematics 2 Science China. Mathematics 1 Discrete Applied Mathematics 1 Information Processing Letters 1 Letters in Mathematical Physics 1 Nuclear Physics. B 1 Fortschritte der Physik 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Calcolo 1 Compositio Mathematica 1 Computing 1 Duke Mathematical Journal 1 Geometriae Dedicata 1 Inventiones Mathematicae 1 Journal of Approximation Theory 1 Journal of Computer and System Sciences 1 Journal of the Mathematical Society of Japan 1 Journal of Number Theory 1 Journal of Soviet Mathematics 1 Mathematics and Computers in Simulation 1 Memoirs of the American Mathematical Society 1 Numerische Mathematik 1 Pacific Journal of Mathematics 1 Results in Mathematics 1 SIAM Journal on Computing 1 SIAM Journal on Numerical Analysis 1 Combinatorica 1 Acta Applicandae Mathematicae 1 Journal of Computer Science and Technology 1 Algorithmica 1 Applied Mathematics Letters 1 MCSS. Mathematics of Control, Signals, and Systems 1 Computational Geometry 1 International Journal of Algebra and Computation 1 Designs, Codes and Cryptography 1 Bulletin of the American Mathematical Society. New Series 1 Mathematical Programming. Series A. Series B 1 Journal of Dynamics and Differential Equations 1 Vestnik St. Petersburg University. Mathematics 1 Cybernetics and Systems Analysis 1 Experimental Mathematics 1 SIAM Journal on Scientific Computing 1 Journal of Algebraic Geometry 1 Journal de Théorie des Nombres de Bordeaux 1 Discrete and Continuous Dynamical Systems 1 Transformation Groups 1 Multibody System Dynamics 1 Mathematical Physics, Analysis and Geometry 1 Journal of the ACM 1 Annals of Combinatorics 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Nonlinear Mathematical Physics 1 Nonlinear Analysis. Real World Applications 1 Dynamical Systems 1 Discrete and Continuous Dynamical Systems. Series B 1 Communications on Pure and Applied Analysis 1 Oberwolfach Reports 1 Advances in High Energy Physics ...and 7 more Serials all top 5 Cited in 44 Fields 166 Computer science (68-XX) 148 Commutative algebra (13-XX) 96 Numerical analysis (65-XX) 75 Field theory and polynomials (12-XX) 67 Algebraic geometry (14-XX) 52 Ordinary differential equations (34-XX) 35 Number theory (11-XX) 21 Linear and multilinear algebra; matrix theory (15-XX) 20 Dynamical systems and ergodic theory (37-XX) 13 Real functions (26-XX) 13 Functions of a complex variable (30-XX) 12 Operations research, mathematical programming (90-XX) 11 Special functions (33-XX) 10 Associative rings and algebras (16-XX) 10 Quantum theory (81-XX) 8 Several complex variables and analytic spaces (32-XX) 8 Approximations and expansions (41-XX) 7 Combinatorics (05-XX) 6 Partial differential equations (35-XX) 6 Information and communication theory, circuits (94-XX) 5 Difference and functional equations (39-XX) 4 Mathematical logic and foundations (03-XX) 4 Group theory and generalizations (20-XX) 4 Biology and other natural sciences (92-XX) 3 Convex and discrete geometry (52-XX) 3 Mechanics of particles and systems (70-XX) 3 Relativity and gravitational theory (83-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Functional analysis (46-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geometry (51-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Systems theory; control (93-XX) 1 \(K\)-theory (19-XX) 1 Topological groups, Lie groups (22-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) Citations by Year