Edit Profile (opens in new tab) Singer, Michael F. Co-Author Distance Author ID: singer.michael-f Published as: Singer, Michael F.; Singer, M. F.; Singer, Michael; Singer, M. more...less Homepage: https://singer.math.ncsu.edu/ External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · dblp · GND Videos: carmin.tv Documents Indexed: 108 Publications since 1975, including 5 Books and 5 Additional arXiv Preprints 2 Contributions as Editor · 1 Further Contribution Reviewing Activity: 26 Reviews Biographic References: 1 Publication Co-Authors: 49 Co-Authors with 82 Joint Publications 1,211 Co-Co-Authors all top 5 Co-Authors 24 single-authored 8 Chen, Shaoshi 8 Hardouin, Charlotte 8 Ulmer, Felix 7 Mitschi, Claude 6 Grigor’ev, Dmitriĭ Yur’evich 6 Schecter, Stephen 5 Feng, Ruyong 5 Rubel, Lee Albert 4 Cassidy, Phyllis Joan 4 Karpinski, Marek 4 Roques, Julien 3 Dreyfus, Thomas 3 Henson, C. Ward 3 Kauers, Manuel 3 Li, Ziming 3 Tretkoff, Marvin D. 3 Wu, Min 2 Caviness, Bob F. 2 Churchill, Richard C. 2 Compoint, Elie 2 Cormier, Olivier 2 Davenport, James Harold 2 Kottke, Chris 2 Minchenko, Andrey 2 Ovchinnikov, Alexey Igorevich 2 Prelle, M. J. 2 Rod, David L. 2 Saunders, B. David 2 Schäfke, Reinhard 2 van den Dries, Lou 2 van der Put, Marius 1 Arreche, Carlos E. 1 Baider, Alberto 1 Bass, Hyman 1 Berman, P. H. 1 Buium, Alexandru 1 Chatzidakis, Zoé Maria 1 Cook, William Jeffrey 1 Fine, Joel 1 Fritzsch, Karsten 1 Haimo, Franklin 1 Hendriks, Peter A. 1 Hubert, Evelyne 1 Jaroschek, Maximilian 1 Jiménez-Pastor, Antonio 1 Kolchin, Ellis Robert 1 Krasnov, Kirill V. 1 Ma, Pingchuan 1 Mazzeo, Rafe R. 1 Melrose, Richard Burt 1 Pillwein, Veronika 1 Poizat, Bruno Petrovich 1 Raab, Clemens G. 1 Rosenlicht, Maxwell 1 Sauloy, Jacques 1 Trager, Barry M. 1 Watt, Stephen Michael 1 Yao, Andrew Chi-Chih 1 Zheng, Dabin all top 5 Serials 11 Journal of Symbolic Computation 7 Proceedings of the American Mathematical Society 5 American Journal of Mathematics 5 Journal of Algebra 5 Transactions of the American Mathematical Society 4 Journal of Pure and Applied Algebra 4 SIAM Journal on Computing 3 Mathematische Annalen 3 Advances in Applied Mathematics 2 Acta Mathematica 2 Bulletin of the London Mathematical Society 2 Journal of Differential Equations 2 Pacific Journal of Mathematics 2 Complex Variables. Theory and Application 2 Applicable Algebra in Engineering, Communication and Computing 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Selecta Mathematica. New Series 1 Communications in Algebra 1 Inventiones Mathematicae 1 Journal of Combinatorial Theory. Series A 1 The Journal of Symbolic Logic 1 Memoirs of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 IMRN. International Mathematics Research Notices 1 Journal of the European Mathematical Society (JEMS) 1 Foundations of Computational Mathematics 1 Journal of the Institute of Mathematics of Jussieu 1 Grundlehren der Mathematischen Wissenschaften 1 Lecture Notes in Mathematics 1 Mathematical Surveys and Monographs 1 Texts & Monographs in Symbolic Computation 1 Annales Henri Lebesgue 1 Computational Mathematics and Applications all top 5 Fields 75 Field theory and polynomials (12-XX) 47 Ordinary differential equations (34-XX) 28 Computer science (68-XX) 12 Difference and functional equations (39-XX) 9 Functions of a complex variable (30-XX) 8 Special functions (33-XX) 7 Dynamical systems and ergodic theory (37-XX) 5 Combinatorics (05-XX) 5 Number theory (11-XX) 5 Commutative algebra (13-XX) 5 Manifolds and cell complexes (57-XX) 4 General and overarching topics; collections (00-XX) 4 Mathematical logic and foundations (03-XX) 4 Algebraic geometry (14-XX) 4 Associative rings and algebras (16-XX) 4 Group theory and generalizations (20-XX) 4 Real functions (26-XX) 3 Probability theory and stochastic processes (60-XX) 3 Numerical analysis (65-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 2 Partial differential equations (35-XX) 2 Operator theory (47-XX) 2 Differential geometry (53-XX) 2 Mechanics of particles and systems (70-XX) 1 Nonassociative rings and algebras (17-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 97 Publications have been cited 2,120 times in 1,211 Documents Cited by ▼ Year ▼ Galois theory of linear differential equations. Zbl 1036.12008 van der Put, Marius; Singer, Michael F. 423 2003 Liouvillian first integrals of differential equations. Zbl 0756.12006 Singer, Michael F. 171 1992 Galois theory of difference equations. Zbl 0930.12006 van der Put, Marius; Singer, Michael F. 142 1997 Elementary first integrals of differential equations. Zbl 0527.12016 Prelle, M. J.; Singer, M. F. 141 1983 Differential Galois theory of linear difference equations. Zbl 1163.12002 Hardouin, Charlotte; Singer, Michael F. 75 2008 Solving difference equations in finite terms. Zbl 0930.39004 Hendriks, Peter A.; Singer, Michael F. 56 1999 Liouvillian solutions of \(n\)-th order homogeneous linear differential equations. Zbl 0477.12026 Singer, Michael F. 54 1981 Galois groups of second and third order linear differential equations. Zbl 0802.12004 Singer, Michael F.; Ulmer, Felix 54 1993 Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields. Zbl 0711.68059 Grigoriev, Dima Yu.; Karpinski, Marek; Singer, Michael F. 41 1990 Liouvillian solutions of linear differential equations with Liouvillian coefficients. Zbl 0776.12002 Singer, Michael F. 38 1991 Testing reducibility of linear differential operators: A group theoretic perspective. Zbl 0999.12007 Singer, Michael F. 38 1996 The model theory of ordered differential fields. Zbl 0396.03031 Singer, Michael F. 35 1978 Liouvillian and algebraic solutions of second and third order linear differential equations. Zbl 0802.12005 Singer, Michael F.; Ulmer, Felix 35 1993 On the infinitesimal geometry of integrable systems. Zbl 1005.37510 Baider, A.; Churchill, R. C.; Rod, D. L.; Singer, M. F. 34 1996 On the nature of the generating series of walks in the quarter plane. Zbl 1392.05007 Dreyfus, Thomas; Hardouin, Charlotte; Roques, Julien; Singer, Michael F. 32 2018 An extension of Liouville’s theorem on integration in finite terms. Zbl 0575.12021 Singer, M. F.; Saunders, B. D.; Caviness, B. F. 26 1985 Residues and telescopers for bivariate rational functions. Zbl 1248.33042 Chen, Shaoshi; Singer, Michael F. 24 2012 Solving ordinary differential equations in terms of series with real exponents. Zbl 0758.12004 Grigor’ev, D. Yu.; Singer, M. F. 23 1991 Telescopers for rational and algebraic functions via residues. Zbl 1323.68592 Chen, Shaoshi; Kauers, Manuel; Singer, Michael F. 21 2012 Solving homogeneous linear differential equations in terms of second order linear differential equations. Zbl 0564.12022 Singer, Michael F. 21 1985 Computing Galois groups of completely reducible differential equations. Zbl 0997.12009 Compoint, Elie; Singer, Michael F. 21 1999 Galois theory of parameterized differential equations and linear differential algebraic groups. Zbl 1356.12004 Cassidy, Phyllis J.; Singer, Michael F. 20 2007 Galois theory of parameterized differential equations and linear differential algebraic groups. Zbl 1230.12003 Cassidy, Phyllis J.; Singer, Michael F. 20 2007 Algebraic solutions of \(n\)-th order linear differential equations. Zbl 0453.12010 Singer, Michael F. 19 1980 A Jordan-Hölder theorem for differential algebraic groups. Zbl 1234.12003 Cassidy, Phyllis J.; Singer, Michael F. 19 2011 Introduction to the Galois theory of linear differential equations. Zbl 1176.12005 Singer, Michael F. 19 2009 Moduli of linear differential equations on the Riemann sphere with fixed Galois groups. Zbl 0778.12007 Singer, Michael F. 19 1993 Unipotent differential algebraic groups as parameterized differential Galois groups. Zbl 1364.12005 Minchenko, Andrey; Ovchinnikov, Alexey; Singer, Michael F. 18 2014 Necessary conditions for Liouvillian solutions of (third order) linear differential equations. Zbl 0813.12003 Singer, Michael F.; Ulmer, Felix 18 1995 Walks in the quarter plane: genus zero case. Zbl 1439.05015 Dreyfus, Thomas; Hardouin, Charlotte; Roques, Julien; Singer, Michael F. 17 2020 Desingularization explains order-degree curves for Ore operators. Zbl 1360.68927 Chen, Shaoshi; Jaroschek, Maximilian; Kauers, Manuel; Singer, Michael F. 16 2013 Linear differential operators for polynomial equations. Zbl 1030.12002 Cormier, Olivier; Singer, Michael F.; Trager, Barry M.; Ulmer, Felix 16 2002 Computational complexity of sparse rational interpolation. Zbl 0802.68060 Grigoriev, Dima; Karpinski, Marek; Singer, Michael F. 16 1994 An outline of differential Galois theory. Zbl 0713.12005 Singer, Michael F. 16 1988 Connected linear groups as differential Galois groups. Zbl 0867.12004 Mitschi, C.; Singer, M. F. 16 1996 Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations. Zbl 1339.12003 Minchenko, Andrey; Ovchinnikov, Alexey; Singer, Michael F. 15 2015 Consistent systems of linear differential and difference equations. Zbl 1425.39003 Schäfke, Reinhard; Singer, Michael F. 15 2019 On the definitions of difference Galois groups. Zbl 1234.12005 Chatzidakis, Zoé; Hardouin, Charlotte; Singer, Michael F. 15 2008 Selected works of Ellis Kolchin with commentary. Ed. by Hyman Bass, Alexandru Buium and Phyllis J. Cassidy. Zbl 0930.12004 Kolchin, Ellis 15 1999 Monodromy groups of parameterized linear differential equations with regular singularities. Zbl 1254.34124 Mitschi, Claude; Singer, Michael F. 14 2012 Desingularization of Ore operators. Zbl 1348.68300 Chen, Shaoshi; Kauers, Manuel; Singer, Michael F. 14 2016 Group-theoretic obstructions to integrability. Zbl 0824.58021 Churchill, R. C.; Rod, D. L.; Singer, M. F. 13 1995 Linear algebraic groups as parameterized Picard-Vessiot Galois groups. Zbl 1296.12003 Singer, Michael F. 13 2013 Algebraic relations among solutions of linear differential equations. Zbl 0593.12014 Singer, Michael F. 12 1986 Formal solutions of differential equations. Zbl 0727.12011 Singer, Michael F. 12 1990 Calculating the Galois group of \(L_1(L_2(y))=0,\) \(L_1, L_2\) completely reducible operators. Zbl 0931.12009 Berman, P. H.; Singer, M. F. 12 1999 A class of differential fields with minimal differential closures. Zbl 0396.03032 Singer, Michael F. 10 1978 Planar polynomial foliations. Zbl 0434.57018 Schecter, Stephen; Singer, Michael F. 10 1980 On elementary, generalized elementary, and Liouvillian extension fields. Zbl 0369.12016 Rosenlicht, Maxwell; Singer, Michael 10 1977 Solvable-by-finite groups as differential Galois groups. Zbl 1066.12003 Mitschi, Claude; Singer, Michael F. 10 2002 Linear differential equations and products of linear forms. Zbl 0908.12003 Singer, Michael F.; Ulmer, Felix 10 1997 The interpolation problem for \(k\)-sparse sums of eigenfunctions of operators. Zbl 0785.12004 Grigoriev, Dima Yu.; Karpinski, Marek; Singer, Michael F. 9 1991 On the summability of bivariate rational functions. Zbl 1301.33003 Chen, Shaoshi; Singer, Michael F. 9 2014 Galois groups for integrable and projectively integrable linear difference equations. Zbl 1364.39002 Arreche, Carlos E.; Singer, Michael F. 9 2017 Solutions of linear differential equations in function fields of one variable. Zbl 0318.12106 Singer, Michael F. 8 1976 Elementary solutions of differential equations. Zbl 0315.12103 Singer, Michael F. 8 1975 Algebraic relations among solutions of linear differential equations: Fano’s theorem. Zbl 0651.12016 Singer, Michael F. 8 1988 Parallel telescoping and parameterized Picard-Vessiot theory. Zbl 1325.68269 Chen, Shaoshi; Feng, Ruyong; Li, Ziming; Singer, Michael F. 7 2014 Elementary and Liouvillian solutions of linear differential equations. Zbl 0652.12016 Davenport, J. H.; Singer, M. F. 7 1986 Separatrices at singular points of planar vector fields. Zbl 0455.58020 Schecter, Stephen; Singer, Michael F. 6 1980 Model theory of partial differential fields: from commuting to noncommuting derivations. Zbl 1108.03044 Singer, Michael F. 6 2007 A recursive method for determining the one-dimensional submodules of Laurent-Ore modules. Zbl 1356.12012 Li, Ziming; Singer, Michael F.; Wu, Min; Zheng, Dabin 6 2006 Galois theories of linear difference equations: an introduction. Zbl 1345.39001 Hardouin, Charlotte; Sauloy, Jacques; Singer, Michael F. 6 2016 A differentially algebraic elimination theorem with application to analog computability in the calculus of variations. Zbl 0582.34011 Rubel, Lee A.; Singer, Michael F. 6 1985 On differentially algebraic generating series for walks in the quarter plane. Zbl 1476.05013 Hardouin, Charlotte; Singer, Michael F. 6 2021 Autonomous functions. Zbl 0674.34004 Rubel, Lee A.; Singer, Michael F. 6 1988 Some structural results on \(\mathrm{D}^n\)-finite functions. Zbl 1480.12006 Jiménez-Pastor, Antonio; Pillwein, Veronika; Singer, Michael F. 6 2020 Algebraic and algorithmic aspects of linear difference equations. Zbl 1347.39002 Singer, Michael F. 5 2016 Computational complexity of sparse real algebraic function interpolation. Zbl 0801.68087 Grigoriev, D.; Karpinski, M.; Singer, M. F. 5 1993 Liouvillian solutions of linear difference-differential equations. Zbl 1233.12004 Feng, Ruyong; Singer, Michael F.; Wu, Min 4 2010 A class of vectorfields on \(S^ 2\) that are topologically equivalent to polynomial vectorfields. Zbl 0523.58033 Schecter, Stephen; Singer, Michael F. 4 1985 On the constructive inverse problem in differential Galois theory. Zbl 1088.34075 Cook, William J.; Mitschi, Claude; Singer, Michael F. 4 2005 Linear relations between the solutions of a differential equation. (Relations linéaires entre solutions d’une équation différentielle.) Zbl 1041.12500 Compoint, Élie; Singer, Michael 4 1998 Projective isomonodromy and Galois groups. Zbl 1268.34187 Mitschi, Claude; Singer, Michael F. 4 2013 Functions satisfying elementary relations. Zbl 0351.12101 Singer, Michael F. 3 1977 Singular points of planar vector fields. Zbl 0447.58022 Schecter, Stephen; Singer, Michael F. 3 1980 An extension of Liouville’s theorem on integration in finite terms. Zbl 0482.12008 Singer, M. F.; Saunders, B. D.; Caviness, B. F. 3 1981 Partial compactification of monopoles and metric asymptotics. Zbl 1529.81118 Kottke, Chris; Singer, Michael 3 2022 Algebraic properties of the ring of general exponential polynomials. Zbl 0647.32003 Henson, C. Ward; Rubel, Lee A.; Singer, Michael F. 3 1989 Correction to ”Separatrices at singular points of planar vector fields”. Zbl 0529.58018 Schecter, Stephen; Singer, Michael F. 2 1983 A classification of differential equations of Fuchsian class. Zbl 0576.34001 Singer, Michael F.; Tretkoff, Marvin D. 2 1985 Some applications of linear groups to differential equations. Zbl 0577.34004 Singer, Michael F.; Tretkoff, Marvin D. 2 1985 An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations. Zbl 1233.12005 Feng, Ruyong; Singer, Michael F.; Wu, Min 2 2010 Computing the Galois group of a polynomial using linear differential equations. Zbl 1326.68349 Cormier, Olivier; Singer, Michael F.; Ulmer, Felix 2 2000 Liouvillian solutions of linear differential equations with Liouvillian coefficients. Zbl 0673.34005 Singer, Michael F. 2 1989 On Ramis’s solution of the local inverse problem of differential Galois theory. Zbl 0854.12001 Mitschi, C.; Singer, M. F. 2 1996 On a third order differential equation whose differential Galois group is the simple group of 168 elements. Zbl 0813.12002 Singer, Michael F.; Ulmer, Felix 2 1993 On computing algebraic functions using logarithms and exponentials. Zbl 0834.68054 Grigoriev, Dima; Singer, Michael; Yao, Andrew 2 1995 Elementary first integrals of differential equations. Zbl 0487.12016 Prelle, M. J.; Singer, M. F. 1 1981 Remarks on analytic continuation. Zbl 0447.30003 Haimo, F.; Singer, M. F.; Tretkoff, M. 1 1980 Elementary and Liouvillian solutions of linear differential equations. Zbl 0609.12024 Singer, M. F.; Davenport, J. H. 1 1985 Erratum to: Differential Galois theory of linear difference equations. Zbl 1228.12005 Hardouin, Charlotte; Singer, Michael F. 1 2011 Liouvillian solutions of third order linear differential equations: new bounds and necessary conditions (extended abstract). Zbl 1058.34503 Singer, Michael F.; Ulmer, Felix 1 1992 On the kernel curves associated with walks in the quarter plane. Zbl 1504.05019 Dreyfus, Thomas; Hardouin, Charlotte; Roques, Julien; Singer, Michael F. 1 2021 Integration in finite terms: fundamental sources. Zbl 1490.26001 1 2022 Sparse interpolation in terms of multivariate Chebyshev polynomials. Zbl 1504.13009 Hubert, Evelyne; Singer, Michael F. 1 2022 Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition. Zbl 1462.53044 Fine, Joel; Krasnov, Kirill; Singer, Michael 1 2021 Partial compactification of monopoles and metric asymptotics. Zbl 1529.81118 Kottke, Chris; Singer, Michael 3 2022 Integration in finite terms: fundamental sources. Zbl 1490.26001 1 2022 Sparse interpolation in terms of multivariate Chebyshev polynomials. Zbl 1504.13009 Hubert, Evelyne; Singer, Michael F. 1 2022 On differentially algebraic generating series for walks in the quarter plane. Zbl 1476.05013 Hardouin, Charlotte; Singer, Michael F. 6 2021 On the kernel curves associated with walks in the quarter plane. Zbl 1504.05019 Dreyfus, Thomas; Hardouin, Charlotte; Roques, Julien; Singer, Michael F. 1 2021 Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition. Zbl 1462.53044 Fine, Joel; Krasnov, Kirill; Singer, Michael 1 2021 Walks in the quarter plane: genus zero case. Zbl 1439.05015 Dreyfus, Thomas; Hardouin, Charlotte; Roques, Julien; Singer, Michael F. 17 2020 Some structural results on \(\mathrm{D}^n\)-finite functions. Zbl 1480.12006 Jiménez-Pastor, Antonio; Pillwein, Veronika; Singer, Michael F. 6 2020 Consistent systems of linear differential and difference equations. Zbl 1425.39003 Schäfke, Reinhard; Singer, Michael F. 15 2019 On the nature of the generating series of walks in the quarter plane. Zbl 1392.05007 Dreyfus, Thomas; Hardouin, Charlotte; Roques, Julien; Singer, Michael F. 32 2018 Galois groups for integrable and projectively integrable linear difference equations. Zbl 1364.39002 Arreche, Carlos E.; Singer, Michael F. 9 2017 Desingularization of Ore operators. Zbl 1348.68300 Chen, Shaoshi; Kauers, Manuel; Singer, Michael F. 14 2016 Galois theories of linear difference equations: an introduction. Zbl 1345.39001 Hardouin, Charlotte; Sauloy, Jacques; Singer, Michael F. 6 2016 Algebraic and algorithmic aspects of linear difference equations. Zbl 1347.39002 Singer, Michael F. 5 2016 Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations. Zbl 1339.12003 Minchenko, Andrey; Ovchinnikov, Alexey; Singer, Michael F. 15 2015 Unipotent differential algebraic groups as parameterized differential Galois groups. Zbl 1364.12005 Minchenko, Andrey; Ovchinnikov, Alexey; Singer, Michael F. 18 2014 On the summability of bivariate rational functions. Zbl 1301.33003 Chen, Shaoshi; Singer, Michael F. 9 2014 Parallel telescoping and parameterized Picard-Vessiot theory. Zbl 1325.68269 Chen, Shaoshi; Feng, Ruyong; Li, Ziming; Singer, Michael F. 7 2014 Desingularization explains order-degree curves for Ore operators. Zbl 1360.68927 Chen, Shaoshi; Jaroschek, Maximilian; Kauers, Manuel; Singer, Michael F. 16 2013 Linear algebraic groups as parameterized Picard-Vessiot Galois groups. Zbl 1296.12003 Singer, Michael F. 13 2013 Projective isomonodromy and Galois groups. Zbl 1268.34187 Mitschi, Claude; Singer, Michael F. 4 2013 Residues and telescopers for bivariate rational functions. Zbl 1248.33042 Chen, Shaoshi; Singer, Michael F. 24 2012 Telescopers for rational and algebraic functions via residues. Zbl 1323.68592 Chen, Shaoshi; Kauers, Manuel; Singer, Michael F. 21 2012 Monodromy groups of parameterized linear differential equations with regular singularities. Zbl 1254.34124 Mitschi, Claude; Singer, Michael F. 14 2012 A Jordan-Hölder theorem for differential algebraic groups. Zbl 1234.12003 Cassidy, Phyllis J.; Singer, Michael F. 19 2011 Erratum to: Differential Galois theory of linear difference equations. Zbl 1228.12005 Hardouin, Charlotte; Singer, Michael F. 1 2011 Liouvillian solutions of linear difference-differential equations. Zbl 1233.12004 Feng, Ruyong; Singer, Michael F.; Wu, Min 4 2010 An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations. Zbl 1233.12005 Feng, Ruyong; Singer, Michael F.; Wu, Min 2 2010 Introduction to the Galois theory of linear differential equations. Zbl 1176.12005 Singer, Michael F. 19 2009 Differential Galois theory of linear difference equations. Zbl 1163.12002 Hardouin, Charlotte; Singer, Michael F. 75 2008 On the definitions of difference Galois groups. Zbl 1234.12005 Chatzidakis, Zoé; Hardouin, Charlotte; Singer, Michael F. 15 2008 Galois theory of parameterized differential equations and linear differential algebraic groups. Zbl 1356.12004 Cassidy, Phyllis J.; Singer, Michael F. 20 2007 Galois theory of parameterized differential equations and linear differential algebraic groups. Zbl 1230.12003 Cassidy, Phyllis J.; Singer, Michael F. 20 2007 Model theory of partial differential fields: from commuting to noncommuting derivations. Zbl 1108.03044 Singer, Michael F. 6 2007 A recursive method for determining the one-dimensional submodules of Laurent-Ore modules. Zbl 1356.12012 Li, Ziming; Singer, Michael F.; Wu, Min; Zheng, Dabin 6 2006 On the constructive inverse problem in differential Galois theory. Zbl 1088.34075 Cook, William J.; Mitschi, Claude; Singer, Michael F. 4 2005 Galois theory of linear differential equations. Zbl 1036.12008 van der Put, Marius; Singer, Michael F. 423 2003 Linear differential operators for polynomial equations. Zbl 1030.12002 Cormier, Olivier; Singer, Michael F.; Trager, Barry M.; Ulmer, Felix 16 2002 Solvable-by-finite groups as differential Galois groups. Zbl 1066.12003 Mitschi, Claude; Singer, Michael F. 10 2002 Computing the Galois group of a polynomial using linear differential equations. Zbl 1326.68349 Cormier, Olivier; Singer, Michael F.; Ulmer, Felix 2 2000 Solving difference equations in finite terms. Zbl 0930.39004 Hendriks, Peter A.; Singer, Michael F. 56 1999 Computing Galois groups of completely reducible differential equations. Zbl 0997.12009 Compoint, Elie; Singer, Michael F. 21 1999 Selected works of Ellis Kolchin with commentary. Ed. by Hyman Bass, Alexandru Buium and Phyllis J. Cassidy. Zbl 0930.12004 Kolchin, Ellis 15 1999 Calculating the Galois group of \(L_1(L_2(y))=0,\) \(L_1, L_2\) completely reducible operators. Zbl 0931.12009 Berman, P. H.; Singer, M. F. 12 1999 Linear relations between the solutions of a differential equation. (Relations linéaires entre solutions d’une équation différentielle.) Zbl 1041.12500 Compoint, Élie; Singer, Michael 4 1998 Galois theory of difference equations. Zbl 0930.12006 van der Put, Marius; Singer, Michael F. 142 1997 Linear differential equations and products of linear forms. Zbl 0908.12003 Singer, Michael F.; Ulmer, Felix 10 1997 Testing reducibility of linear differential operators: A group theoretic perspective. Zbl 0999.12007 Singer, Michael F. 38 1996 On the infinitesimal geometry of integrable systems. Zbl 1005.37510 Baider, A.; Churchill, R. C.; Rod, D. L.; Singer, M. F. 34 1996 Connected linear groups as differential Galois groups. Zbl 0867.12004 Mitschi, C.; Singer, M. F. 16 1996 On Ramis’s solution of the local inverse problem of differential Galois theory. Zbl 0854.12001 Mitschi, C.; Singer, M. F. 2 1996 Necessary conditions for Liouvillian solutions of (third order) linear differential equations. Zbl 0813.12003 Singer, Michael F.; Ulmer, Felix 18 1995 Group-theoretic obstructions to integrability. Zbl 0824.58021 Churchill, R. C.; Rod, D. L.; Singer, M. F. 13 1995 On computing algebraic functions using logarithms and exponentials. Zbl 0834.68054 Grigoriev, Dima; Singer, Michael; Yao, Andrew 2 1995 Computational complexity of sparse rational interpolation. Zbl 0802.68060 Grigoriev, Dima; Karpinski, Marek; Singer, Michael F. 16 1994 Galois groups of second and third order linear differential equations. Zbl 0802.12004 Singer, Michael F.; Ulmer, Felix 54 1993 Liouvillian and algebraic solutions of second and third order linear differential equations. Zbl 0802.12005 Singer, Michael F.; Ulmer, Felix 35 1993 Moduli of linear differential equations on the Riemann sphere with fixed Galois groups. Zbl 0778.12007 Singer, Michael F. 19 1993 Computational complexity of sparse real algebraic function interpolation. Zbl 0801.68087 Grigoriev, D.; Karpinski, M.; Singer, M. F. 5 1993 On a third order differential equation whose differential Galois group is the simple group of 168 elements. Zbl 0813.12002 Singer, Michael F.; Ulmer, Felix 2 1993 Liouvillian first integrals of differential equations. Zbl 0756.12006 Singer, Michael F. 171 1992 Liouvillian solutions of third order linear differential equations: new bounds and necessary conditions (extended abstract). Zbl 1058.34503 Singer, Michael F.; Ulmer, Felix 1 1992 Liouvillian solutions of linear differential equations with Liouvillian coefficients. Zbl 0776.12002 Singer, Michael F. 38 1991 Solving ordinary differential equations in terms of series with real exponents. Zbl 0758.12004 Grigor’ev, D. Yu.; Singer, M. F. 23 1991 The interpolation problem for \(k\)-sparse sums of eigenfunctions of operators. Zbl 0785.12004 Grigoriev, Dima Yu.; Karpinski, Marek; Singer, Michael F. 9 1991 Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields. Zbl 0711.68059 Grigoriev, Dima Yu.; Karpinski, Marek; Singer, Michael F. 41 1990 Formal solutions of differential equations. Zbl 0727.12011 Singer, Michael F. 12 1990 Algebraic properties of the ring of general exponential polynomials. Zbl 0647.32003 Henson, C. Ward; Rubel, Lee A.; Singer, Michael F. 3 1989 Liouvillian solutions of linear differential equations with Liouvillian coefficients. Zbl 0673.34005 Singer, Michael F. 2 1989 An outline of differential Galois theory. Zbl 0713.12005 Singer, Michael F. 16 1988 Algebraic relations among solutions of linear differential equations: Fano’s theorem. Zbl 0651.12016 Singer, Michael F. 8 1988 Autonomous functions. Zbl 0674.34004 Rubel, Lee A.; Singer, Michael F. 6 1988 Algebraic relations among solutions of linear differential equations. Zbl 0593.12014 Singer, Michael F. 12 1986 Elementary and Liouvillian solutions of linear differential equations. Zbl 0652.12016 Davenport, J. H.; Singer, M. F. 7 1986 An extension of Liouville’s theorem on integration in finite terms. Zbl 0575.12021 Singer, M. F.; Saunders, B. D.; Caviness, B. F. 26 1985 Solving homogeneous linear differential equations in terms of second order linear differential equations. Zbl 0564.12022 Singer, Michael F. 21 1985 A differentially algebraic elimination theorem with application to analog computability in the calculus of variations. Zbl 0582.34011 Rubel, Lee A.; Singer, Michael F. 6 1985 A class of vectorfields on \(S^ 2\) that are topologically equivalent to polynomial vectorfields. Zbl 0523.58033 Schecter, Stephen; Singer, Michael F. 4 1985 A classification of differential equations of Fuchsian class. Zbl 0576.34001 Singer, Michael F.; Tretkoff, Marvin D. 2 1985 Some applications of linear groups to differential equations. Zbl 0577.34004 Singer, Michael F.; Tretkoff, Marvin D. 2 1985 Elementary and Liouvillian solutions of linear differential equations. Zbl 0609.12024 Singer, M. F.; Davenport, J. H. 1 1985 Elementary first integrals of differential equations. Zbl 0527.12016 Prelle, M. J.; Singer, M. F. 141 1983 Correction to ”Separatrices at singular points of planar vector fields”. Zbl 0529.58018 Schecter, Stephen; Singer, Michael F. 2 1983 Liouvillian solutions of \(n\)-th order homogeneous linear differential equations. Zbl 0477.12026 Singer, Michael F. 54 1981 An extension of Liouville’s theorem on integration in finite terms. Zbl 0482.12008 Singer, M. F.; Saunders, B. D.; Caviness, B. F. 3 1981 Elementary first integrals of differential equations. Zbl 0487.12016 Prelle, M. J.; Singer, M. F. 1 1981 Algebraic solutions of \(n\)-th order linear differential equations. Zbl 0453.12010 Singer, Michael F. 19 1980 Planar polynomial foliations. Zbl 0434.57018 Schecter, Stephen; Singer, Michael F. 10 1980 Separatrices at singular points of planar vector fields. Zbl 0455.58020 Schecter, Stephen; Singer, Michael F. 6 1980 Singular points of planar vector fields. Zbl 0447.58022 Schecter, Stephen; Singer, Michael F. 3 1980 Remarks on analytic continuation. Zbl 0447.30003 Haimo, F.; Singer, M. F.; Tretkoff, M. 1 1980 The model theory of ordered differential fields. Zbl 0396.03031 Singer, Michael F. 35 1978 A class of differential fields with minimal differential closures. Zbl 0396.03032 Singer, Michael F. 10 1978 On elementary, generalized elementary, and Liouvillian extension fields. Zbl 0369.12016 Rosenlicht, Maxwell; Singer, Michael 10 1977 Functions satisfying elementary relations. Zbl 0351.12101 Singer, Michael F. 3 1977 Solutions of linear differential equations in function fields of one variable. Zbl 0318.12106 Singer, Michael F. 8 1976 Elementary solutions of differential equations. Zbl 0315.12103 Singer, Michael F. 8 1975 all cited Publications top 5 cited Publications all top 5 Cited by 1,005 Authors 65 Llibre, Jaume 45 Singer, Michael F. 30 Giné, Jaume 30 Valls Anglés, Cláudia 22 Schneider, Carsten 21 van der Put, Marius 20 Guo, Li 19 Maciejewski, Andrzej J. 18 Bostan, Alin 18 Chen, Shaoshi 18 Weil, Jacques-Arthur 17 Przybylska, Maria 17 Roques, Julien 17 Wibmer, Michael 16 Feng, Ruyong 15 Barkatou, Moulay A. 15 Dreyfus, Thomas 15 Hardouin, Charlotte 15 Li, Ziming 15 Ovchinnikov, Alexey Igorevich 14 Abramov, Sergeĭ Aleksandrovich 14 Acosta Humánez, Primitivo Belén 14 Demina, Maria V. 14 Grigor’ev, Dmitriĭ Yur’evich 14 Yagasaki, Kazuyuki 14 Zhang, Xiang 13 Kauers, Manuel 13 van Hoeij, Mark 12 Ulmer, Felix 11 Bronstein, Manuel Eric 11 Cluzeau, Thomas 11 Gao, Xing 11 León Sánchez, Omar 10 Algaba, Antonio 10 Bachmayr, Annette 10 da Mota, Luis Antonio Campinho Pereira 10 Duarte, L. G. S. 10 García, Cristóbal 10 Morales-Ruiz, Juan José 10 Pantazi, Chara 10 Shi, Shaoyun 9 Blümlein, Johannes 9 Casale, Guy 9 Combot, Thierry 9 Crespo Vicente, Teresa 9 Di Vizio, Lucia 9 Gao, Xiaoshan 9 Hajto, Zbigniew 9 Juan, Lourdes 9 Karpinski, Marek 9 Point, Françoise 9 Rosenkranz, Markus 9 Srinivasan, Varadharaj Ravi 9 Top, Jaap 8 Arreche, Carlos E. 8 Bousquet-Mélou, Mireille 8 Christov, Ognyan 8 Giacomini, Hector J. 8 Lakshmanan, Muthusamy 8 Li, Wenlei 8 Petkovšek, Marko 8 Raschel, Kilian 8 Reyes, Manuel 8 Rivoal, Tanguy 8 Senthilvelan, Murugaian 8 Zhang, Yi 7 Blázquez-Sanz, David 7 Chandrasekar, V. K. 7 Chèze, Guillaume 7 Christopher, Colin J. 7 Compoint, Elie 7 Duval, Guillaume 7 Ferragut, Antoni 7 Guha, Partha 7 Magid, Andy Roy 7 Pillay, Anand 7 Ramis, Jean-Pierre 7 Shparlinski, Igor E. 7 Szumiński, Wojciech 6 Ablinger, Jakob 6 Freitag, James 6 Ghose Choudhury, Anindya 6 Grau, Maite 6 Harbater, David 6 Hartmann, Julia 6 Jiménez-Pastor, Antonio 6 Koutschan, Christoph 6 Lee, Wen-shin 6 Panferov, Anton A. 6 Salvy, Bruno 6 Sauloy, Jacques 6 Schwarz, Fritz 6 Stachowiak, Tomasz 6 Walcher, Sebastian 5 Avellar, J. 5 Bourlès, Henri 5 Brouette, Quentin 5 Coutinho, S. C. 5 Giesbrecht, Mark W. 5 Gontsov, Renat R. ...and 905 more Authors all top 5 Cited in 273 Serials 88 Journal of Symbolic Computation 48 Journal of Algebra 40 Journal of Differential Equations 28 Advances in Applied Mathematics 25 Annales de l’Institut Fourier 25 Journal of Pure and Applied Algebra 25 Transactions of the American Mathematical Society 23 Proceedings of the American Mathematical Society 21 Journal of Mathematical Physics 19 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 18 Journal of Mathematical Analysis and Applications 18 Qualitative Theory of Dynamical Systems 17 Applicable Algebra in Engineering, Communication and Computing 17 Comptes Rendus. Mathématique. Académie des Sciences, Paris 15 Theoretical Computer Science 14 Communications in Algebra 14 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 12 Physics Letters. A 12 Programming and Computer Software 12 Journal of Systems Science and Complexity 11 Mathematische Annalen 11 Physica D 10 Computer Physics Communications 10 Chaos, Solitons and Fractals 10 Journal of Nonlinear Mathematical Physics 9 Advances in Mathematics 9 Applied Mathematics and Computation 9 Linear Algebra and its Applications 9 Bulletin des Sciences Mathématiques 8 Mathematics of Computation 8 Journal of Geometry and Physics 8 Journal of Algebra and its Applications 7 Journal of Difference Equations and Applications 7 Mathematics in Computer Science 7 Journal of Physics A: Mathematical and Theoretical 6 Communications in Mathematical Physics 6 Israel Journal of Mathematics 6 Rendiconti del Circolo Matemàtico di Palermo. Serie II 6 Journal of Mathematical Sciences (New York) 6 The Electronic Journal of Combinatorics 6 Selecta Mathematica. New Series 6 Discrete and Continuous Dynamical Systems 6 Journal of the European Mathematical Society (JEMS) 6 Arnold Mathematical Journal 5 Rocky Mountain Journal of Mathematics 5 Bulletin of the London Mathematical Society 5 Annals of Pure and Applied Logic 5 Indagationes Mathematicae. New Series 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Communications in Nonlinear Science and Numerical Simulation 5 Journal of Dynamical and Control Systems 4 Information Processing Letters 4 Inventiones Mathematicae 4 Journal of Computational and Applied Mathematics 4 Mathematics and Computers in Simulation 4 Mathematische Zeitschrift 4 Journal of Complexity 4 Applied Mathematics Letters 4 International Journal of Algebra and Computation 4 Celestial Mechanics and Dynamical Astronomy 4 Séminaire Lotharingien de Combinatoire 4 Annals of Combinatorics 4 Regular and Chaotic Dynamics 4 Communications in Contemporary Mathematics 4 Journal of High Energy Physics 4 Nonlinear Analysis. Real World Applications 4 Foundations of Computational Mathematics 4 Journal of the Institute of Mathematics of Jussieu 4 Annales Henri Lebesgue 3 Linear and Multilinear Algebra 3 Nuclear Physics. B 3 Reports on Mathematical Physics 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Journal of Combinatorial Theory. Series A 3 Journal of the London Mathematical Society. Second Series 3 Manuscripta Mathematica 3 Proceedings of the London Mathematical Society. Third Series 3 European Journal of Combinatorics 3 Computational Mathematics and Mathematical Physics 3 Archive for Mathematical Logic 3 The Ramanujan Journal 3 Chaos 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Acta Mathematica Sinica. English Series 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Mediterranean Journal of Mathematics 3 Oberwolfach Reports 3 Algebra & Number Theory 3 ACM Communications in Computer Algebra 3 Science China. Mathematics 3 European Journal of Mathematics 2 American Mathematical Monthly 2 Archive for History of Exact Sciences 2 Letters in Mathematical Physics 2 Nonlinearity 2 Acta Mathematica 2 Bulletin de la Société Mathématique de France 2 Canadian Mathematical Bulletin 2 Compositio Mathematica 2 Functional Analysis and its Applications ...and 173 more Serials all top 5 Cited in 56 Fields 512 Ordinary differential equations (34-XX) 418 Field theory and polynomials (12-XX) 240 Computer science (68-XX) 168 Dynamical systems and ergodic theory (37-XX) 118 Algebraic geometry (14-XX) 105 Commutative algebra (13-XX) 105 Special functions (33-XX) 100 Difference and functional equations (39-XX) 92 Number theory (11-XX) 66 Numerical analysis (65-XX) 63 Associative rings and algebras (16-XX) 57 Mathematical logic and foundations (03-XX) 57 Partial differential equations (35-XX) 55 Combinatorics (05-XX) 55 Mechanics of particles and systems (70-XX) 51 Group theory and generalizations (20-XX) 48 Several complex variables and analytic spaces (32-XX) 33 Quantum theory (81-XX) 29 Nonassociative rings and algebras (17-XX) 25 Functions of a complex variable (30-XX) 18 Approximations and expansions (41-XX) 18 Operator theory (47-XX) 18 Differential geometry (53-XX) 17 Probability theory and stochastic processes (60-XX) 16 Systems theory; control (93-XX) 13 Real functions (26-XX) 12 Biology and other natural sciences (92-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 10 General and overarching topics; collections (00-XX) 9 Category theory; homological algebra (18-XX) 9 Manifolds and cell complexes (57-XX) 9 Information and communication theory, circuits (94-XX) 8 History and biography (01-XX) 8 Topological groups, Lie groups (22-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Relativity and gravitational theory (83-XX) 6 Sequences, series, summability (40-XX) 6 Integral transforms, operational calculus (44-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 General algebraic systems (08-XX) 3 Potential theory (31-XX) 3 Optics, electromagnetic theory (78-XX) 3 Operations research, mathematical programming (90-XX) 2 \(K\)-theory (19-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 General topology (54-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.