Edit Profile (opens in new tab) Abramov, Sergeĭ Aleksandrovich Compute Distance To: Compute Author ID: abramov.sergei-a Published as: Abramov, S. A.; Abramov, Sergei A.; Abramov, Sergei; Abramov, Sergey A.; Abramov, S. Homepage: http://www.ccas.ru/sabramov/ External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru Documents Indexed: 158 Publications since 1971, including 1 Book 2 Contributions as Editor Biographic References: 2 Publications Co-Authors: 35 Co-Authors with 92 Joint Publications 574 Co-Co-Authors all top 5 Co-Authors 64 single-authored 21 Khmelnov, Dennis E. 21 Petkovšek, Marko 15 Ryabenko, Anna A. 13 Barkatou, Moulay A. 6 Bronstein, Manuel Eric 6 Glück, Robert 5 van Hoeij, Mark 4 Rostovtsev, Vitaly A. 3 Bogolyubskaya, A. A. 3 Edneral, Victor F. 3 Gheffar, Amal 3 Kvashenko, K. Yu. 3 Zima, Eugene V. 2 Geddes, Keith O. 2 Kaz’mina, E. A. 2 Kondrat’eva, Marina Vladimirovna 2 Kuklyaeva, V. A. 2 Rozenblyum, M. Yu. 1 Antipov, I. N. 1 Bordachenkova, E. A. 1 Carette, J. J. 1 Gnezdilova, G. G. 1 Klimov, Yuri 1 Kvansenko, K. Yu. 1 Latyshev, Viktor Nikolaevich 1 Mikhalëv, Aleksandr Vasil’evich 1 Ovchinnikov, Alexey Igorevich 1 Paule, Peter 1 Petkovšsek, M. 1 Pflügel, Eckhard 1 Polyakov, S. P. 1 Sevastianov, Leonid A. 1 Tsarev, Sergej Petrovich 1 Zakrajšek, Helena 1 Zobnin, Alexey I. all top 5 Serials 30 Programming and Computer Software 17 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 14 U.S.S.R. Computational Mathematics and Mathematical Physics 11 Journal of Symbolic Computation 8 Computational Mathematics and Mathematical Physics 7 Discrete Mathematics 6 Moscow University Computational Mathematics and Cybernetics 3 Advances in Applied Mathematics 3 Vestnik Moskovskogo Universiteta. Seriya 15 3 Journal of Mathematical Sciences (New York) 3 ACM Communications in Computer Algebra 2 Soviet Mathematics. Doklady 1 Mathematical Notes 1 Journal of Number Theory 1 SIGSAM Bulletin 1 Cybernetics 1 Science of Computer Programming 1 International Journal of Foundations of Computer Science 1 Applicable Algebra in Engineering, Communication and Computing 1 Integral Transforms and Special Functions 1 Journal of Difference Equations and Applications all top 5 Fields 94 Computer science (68-XX) 47 Difference and functional equations (39-XX) 42 Ordinary differential equations (34-XX) 42 Numerical analysis (65-XX) 20 Special functions (33-XX) 13 Field theory and polynomials (12-XX) 6 Number theory (11-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Associative rings and algebras (16-XX) 2 Commutative algebra (13-XX) 2 Algebraic geometry (14-XX) 2 Partial differential equations (35-XX) 2 Operator theory (47-XX) 1 Combinatorics (05-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 96 Publications have been cited 692 times in 232 Documents Cited by ▼ Year ▼ Rational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0719.65063Abramov, S. A. 29 1989 \(q\)-hypergeometric solutions of \(q\)-difference equations. Zbl 0932.33019Abramov, Sergei A.; Paule, Peter; Petkovšek, Marko 29 1998 On polynomial solutions of linear operator equations. Zbl 0914.65132Abramov, Sergei A.; Bronstein, Manuel; Petkovšek, Marko 25 1995 EG-eliminations. Zbl 0936.65144Abramov, Sergei A. 23 1999 Rational solutions of first order linear difference systems. Zbl 0919.65089Abramov, S. A.; Barkatou, M. A. 22 1998 D’Alembertian solutions to linear differential and difference equations. Zbl 0919.34013Abramov, Sergei A.; Petkovšek, Marko 22 1994 On solutions of linear functional systems. Zbl 1356.65245Abramov, Sergei A.; Bronstein, Manuel 22 2001 Rational normal forms and minimal decompositions of hypergeometric terms. Zbl 1005.33010Abramov, S. A.; Petkovšek, M. 18 2002 Rational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0695.65051Abramov, S. A. 18 1989 Indefinite sums of rational functions. Zbl 0914.65133Abramov, S. A. 18 1995 Rational solutions of linear difference and \(q\)-differential equations with polynomial coefficients. Zbl 0910.65107Abramov, S. A. 17 1995 When does Zeilberger’s algorithm succeed? Zbl 1030.33011Abramov, S. A. 16 2003 Rationale Komponente der Lösung einer linearen rekurrenten Relation erster Ordnung mit rationaler rechter Seite. Zbl 0326.65069Abramov, S. A. 16 1975 A criterion for the applicability of Zeilberger’s algorithm to rational functions. Zbl 1023.33017Abramov, S. A.; Le, H. Q. 12 2002 On singular points of solutions of linear differential systems with polynomial coefficients. Zbl 1258.34027Abramov, S. A.; Khmelnov, D. E. 12 2012 Über die Summation rationaler Funktionen. Zbl 0243.65076Abramov, S. A. 12 1971 On the structure of multivariate hypergeometric terms. Zbl 1057.33017Abramov, S. A.; Petkovšek, M. 11 2002 Rational solutions of linear difference and \(q\)-difference equations with polynomial coefficients. Zbl 0914.65131Abramov, S. A. 11 1995 Integration of solutions of linear functional equations. Zbl 0939.34059Abramov, Sergei A.; van Hoeij, Mark 11 1999 Factorization of polynomials and GCD computations for finding universal denominators. Zbl 1202.12004Abramov, S. A.; Gheffar, A.; Khmelnov, D. E. 11 2010 On full rank differential systems with power series coefficients. Zbl 1308.34019Abramov, S. A.; Barkatou, M. A.; Khmelnov, D. E. 10 2015 Rational solutions of linear difference equations: universal denominators and denominator bounds. Zbl 1247.65156Abramov, S. A.; Gheffar, A.; Khmelnov, D. E. 10 2011 On regular and logarithmic solutions of ordinary linear differential systems. Zbl 1169.34301Abramov, S. A.; Bronstein, M.; Khmelnov, D. E. 10 2005 On the dimension of solution spaces of full rank linear differential systems. Zbl 1412.34055Abramov, S. A.; Barkatou, M. A. 9 2013 Linear differential and difference systems: \(\mathrm{EG}_\delta\)- and \(\mathrm{EG}_\sigma\)-eliminations. Zbl 1311.34027Abramov, S. A.; Khmelnov, D. E. 9 2013 Valuations of rational solutions of linear difference equations at irreducible polynomials. Zbl 1221.68298Gheffar, A.; Abramov, S. 9 2011 Higher-order linear differential systems with truncated coefficients. Zbl 1344.68290Abramov, S. A.; Barkatou, M. A.; Pflügel, E. 9 2011 Special formal series solutions of linear operator equations. Zbl 0972.34002Abramov, Sergei A.; Petkovšek, Marko; Ryabenko, Anna 9 2000 Applicability of Zeilberger’s algorithm to hypergeometric terms. Zbl 1072.68642Abramov, S. A. 9 2002 Denominators of rational solutions of linear difference systems of an arbitrary order. Zbl 1261.65134Abramov, S. A.; Khmelnov, D. E. 9 2012 On the summation of rational functions. Zbl 0255.65003Abramov, S. A. 8 1973 D’Alembertian solutions of inhomogeneous linear equations (differential, difference, and some other). Zbl 0966.34005Abramov, Sergei A.; Zima, Eugene V. 8 1996 Ore polynomial rings in one variable in computer algebra. Zbl 1127.16302Abramov, S. A.; Le, H. Q.; Li, Z. 8 2005 Telescoping in the context of symbolic summation in Maple. Zbl 1137.05326Abramov, S. A.; Carette, J. J.; Geddes, K. O.; Le, H. Q. 8 2005 Apparent singularities of linear difference equations with polynomial coefficients. Zbl 1106.39002Abramov, S. A.; Barkatou, M. A.; van Hoeij, M. 7 2006 Problems of computer algebra connected with the search for polynomial solutions of linear differential and difference equations. Zbl 0689.65049Abramov, S. A. 7 1989 Principles of inverse computation and the universal resolving algorithm. Zbl 1026.68023Abramov, Sergei; Glück, Robert 7 2002 On polynomial solutions of linear partial differential and \((q\)-)difference equations. Zbl 1373.68458Abramov, S. A.; Petkovšek, M. 7 2012 Solving linear systems of differential and difference equations with respect to a part of the unknowns. Zbl 1179.65100Abramov, S. A.; Bronstein, M. 7 2006 Minimal decomposition of indefinite hypergeometric sums. Zbl 1356.33012Abramov, Sergei A.; Petkovsek, M. 7 2001 Applicability of Zeilberger’s algorithm to rational functions. Zbl 0963.65026Abramov, S. A.; Le, H. Q. 6 2000 On solution spaces of products of linear differential or difference operators. Zbl 1322.68269Abramov, Sergei A.; Barkatou, Moulay A. 6 2014 Regular solutions of linear differential systems with power series coefficients. Zbl 1317.34019Abramov, S. A.; Khmelnov, D. E. 6 2014 Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients. Zbl 0919.65045Abramov, S. A.; Kvansenko, K. Yu. 6 1991 Analytic solutions of linear difference equations, formal series, and bottom summation. Zbl 1141.68663Abramov, S. A.; Petkovšek, M. 6 2007 Polynomial ring automorphisms, rational \((w,\sigma )\)-canonical forms, and the assignment problem. Zbl 1189.33038Abramov, S. A.; Petkovšek, M. 6 2010 Computable infinite power series in the role of coefficients of linear differential systems. Zbl 1416.68211Abramov, Sergei A.; Barkatou, Moulay A. 6 2014 Search of rational solutions to differential and difference systems by means of formal series. Zbl 1344.34023Abramov, Sergey A. 6 2015 On the differential and full algebraic complexities of operator matrices transformations. Zbl 1453.34014Abramov, Sergei A. 6 2016 Hypergeometric dispersion and the orbit problem. Zbl 1326.68340Abramov, Sergei A.; Bronstein, Manuel 5 2000 The universal resolving algorithm and its correctness: Inverse computation in a functional language. Zbl 1014.68037Abramov, Sergei; Glück, Robert 5 2002 The universal resolving algorithm: Inverse computation in a functional language. Zbl 0963.68500Abramov, Sergei; Glück, Robert 5 2000 Gosper’s algorithm, accurate summation, and the discrete Newton-Leibniz formula. Zbl 1360.33018Abramov, S. A.; Petkovšsek, M. 5 2005 A method for the integration of solutions to Ore equations. Zbl 0919.34011Abramov, Sergei A.; van Hoeij, Mark 5 1997 Linear ordinary differential equations and truncated series. Zbl 1442.34033Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E. 5 2019 Problems of computer algebra involved in the search for polynomial solutions of linear differential and difference equations. Zbl 0723.65048Abramov, S. A. 5 1989 Procedures for searching local solutions of linear differential systems with infinite power series in the role of coefficients. Zbl 1345.34011Abramov, Sergey A.; Ryabenko, Anna A.; Khmelnov, Dennis E. 5 2016 Hypergeometric solutions of first-order linear difference systems with rational-function coefficients. Zbl 1434.33020Abramov, S. A.; Petkovšek, M.; Ryabenko, A. A. 4 2015 A direct algorithm to compute rational solutions of first order linear \(q\)-difference systems. Zbl 0995.65139Abramov, S. A. 4 2002 Subanalytic solutions of linear difference equations and multidimensional hypergeometric sequences. Zbl 1232.39001Abramov, S. A.; Barkatou, M. A.; Van Hoeij, M.; Petkovšek, M. 4 2011 The research seminar on computer algebra in 2009-2010. Zbl 1242.00036Abramov, S. A.; Bogolyubskaya, A. A.; Edneral, V. F.; Rostovtsev, V. A. 3 2011 The scientific research seminar on computer algebra in 1997-1998. Zbl 0972.68814Abramov, S. A.; Rostovtsev, V. A. 3 1998 Computer algebra library for the construction of the minimal telescopers. Zbl 1012.68229Abramov, S. A.; Geddes, K. O.; Le, H. Q. 3 2002 Minimal completely factorable annihilators. Zbl 0929.16045Abramov, Sergei A.; Zima, Eugene 3 1997 On the greatest common divisor of polynomials which depend on a parameter. Zbl 0925.13009Abramov, S. A.; Kvashenko, K. Yu. 3 1993 The set of poles of solutions of linear difference equations with polynomial coefficients. Zbl 1076.39002Abramov, S. A.; van Hoeij, M. 3 2003 An universal resolving algorithm for inverse computation of lazy languages. Zbl 1185.68328Abramov, Sergei; Glück, Robert; Klimov, Yuri 3 2007 Improved universal denominators. Zbl 1147.68877Abramov, S. A.; Polyakov, S. P. 3 2007 Regular solutions of linear ordinary differential equations and truncated series. Zbl 1454.34026Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E. 3 2020 On the summation of \(P\)-recursive sequences. Zbl 1356.33011Abramov, S. A. 3 2006 In memory of Manuel Bronstein. Zbl 1208.01020Abramov, S. A. 2 2006 On valuations of meromorphic solutions of arbitrary-order linear difference systems with polynomial coefficients. Zbl 1323.68577Abramov, S. A.; Khmelnov, D. E. 2 2012 Combining semantics with non-standard interpreter hierarchies. Zbl 1044.68664Abramov, Sergei; Glück, Robert 2 2000 The rational component of the solution of a first-order linear recurrence relation with a rational right side. Zbl 0352.65062Abramov, S. A. 2 1976 Rational canonical forms and efficient representations of hypergeometric terms. Zbl 1072.68643Abramov, S. A.; Le, H. Q.; Petkovšek, M. 2 2003 The research seminar on computer algebra in 2005-2006. Zbl 1137.68300Abramov, S. A.; Bogolyubskaya, A. A.; Rostovtsev, V. A.; Edneral, V. F. 2 2007 Resolving sequences of operators for linear ordinary differential and difference systems of arbitrary order. Zbl 1379.39001Abramov, Sergey A.; Petkovšek, Marko; Ryabenko, Anna A. 2 2016 On rational and hypergeometric solutions of linear ordinary difference equations in \(\Pi\Sigma^\ast\)-field extensions. Zbl 07354271Abramov, Sergei A.; Bronstein, Manuel; Petkovšek, Marko; Schneider, Carsten 2 2021 Indicial rational functions of linear ordinary differential equations with polynomial coefficients. Zbl 1288.34009Abramov, S. A.; Ryabenko, A. A. 1 2009 Rational solutions of linear difference and \(q\)-difference equations with polynomial coefficients. Zbl 0972.68184Abramov, S. A. 1 1999 On peripheral factorization of linear homogeneous operators. Zbl 0973.68667Abramov, S. A.; Tsarev, S. P. 1 1997 From standard to non-standard semantics by semantics modifiers. Zbl 1319.68050Abramov, Sergei; Glück, Robert 1 2001 On d’Alembert substitution. Zbl 0921.34011Abramov, S. A. 1 1993 The denominators of rational solutions to linear difference equations. Zbl 0824.33013Abramov, S. A. 1 1994 Inverse linear difference operators. Zbl 1386.15014Abramov, S. A. 1 2017 The finite-difference second order equation with constant coefficients in the field of rational functions. Zbl 0369.39003Abramov, S. A. 1 1977 On the order of the recurrence produced by the method of creative telescoping. Zbl 1077.33037Abramov, S. A.; Le, H. Q. 1 2005 An algorithm for searching quasirational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0727.65062Abramov, S. A. 1 1991 Dimensions of solution spaces of \(H\)-systems. Zbl 1186.33038Abramov, S. A.; Petkovšek, M. 1 2008 Matrices of scalar differential operators: divisibility and spaces of solutions. Zbl 07264245Abramov, S. A.; Barkatou, M. A.; Petkovšek, M. 1 2020 Revealing matrices of linear differential systems of arbitrary order. Zbl 1455.34002Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E. 1 2017 Procedures for searching Laurent and regular solutions of linear differential equations with the coefficients in the form of truncated power series. Zbl 1462.34028Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E. 1 2020 Truncated series and formal exponential-logarithmic solutions of linear ordinary differential equations. Zbl 07282628Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E. 1 2020 On strongly non-singular polynomial matrices. Zbl 07008083Abramov, Sergei A.; Barkatou, Moulay A. 1 2018 On \(m\)-interlacing solutions of linear difference equations. Zbl 1239.39001Abramov, S. A.; Barkatou, M. A.; Khmelnov, D. E. 1 2009 On unimodular matrices of difference operators. Zbl 1453.65442Abramov, S. A.; Khmelnov, D. E. 1 2018 On rational and hypergeometric solutions of linear ordinary difference equations in \(\Pi\Sigma^\ast\)-field extensions. Zbl 07354271Abramov, Sergei A.; Bronstein, Manuel; Petkovšek, Marko; Schneider, Carsten 2 2021 Regular solutions of linear ordinary differential equations and truncated series. Zbl 1454.34026Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E. 3 2020 Matrices of scalar differential operators: divisibility and spaces of solutions. Zbl 07264245Abramov, S. A.; Barkatou, M. A.; Petkovšek, M. 1 2020 Procedures for searching Laurent and regular solutions of linear differential equations with the coefficients in the form of truncated power series. Zbl 1462.34028Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E. 1 2020 Truncated series and formal exponential-logarithmic solutions of linear ordinary differential equations. Zbl 07282628Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E. 1 2020 Linear ordinary differential equations and truncated series. Zbl 1442.34033Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E. 5 2019 On strongly non-singular polynomial matrices. Zbl 07008083Abramov, Sergei A.; Barkatou, Moulay A. 1 2018 On unimodular matrices of difference operators. Zbl 1453.65442Abramov, S. A.; Khmelnov, D. E. 1 2018 Inverse linear difference operators. Zbl 1386.15014Abramov, S. A. 1 2017 Revealing matrices of linear differential systems of arbitrary order. Zbl 1455.34002Abramov, S. A.; Ryabenko, A. A.; Khmelnov, D. E. 1 2017 On the differential and full algebraic complexities of operator matrices transformations. Zbl 1453.34014Abramov, Sergei A. 6 2016 Procedures for searching local solutions of linear differential systems with infinite power series in the role of coefficients. Zbl 1345.34011Abramov, Sergey A.; Ryabenko, Anna A.; Khmelnov, Dennis E. 5 2016 Resolving sequences of operators for linear ordinary differential and difference systems of arbitrary order. Zbl 1379.39001Abramov, Sergey A.; Petkovšek, Marko; Ryabenko, Anna A. 2 2016 On full rank differential systems with power series coefficients. Zbl 1308.34019Abramov, S. A.; Barkatou, M. A.; Khmelnov, D. E. 10 2015 Search of rational solutions to differential and difference systems by means of formal series. Zbl 1344.34023Abramov, Sergey A. 6 2015 Hypergeometric solutions of first-order linear difference systems with rational-function coefficients. Zbl 1434.33020Abramov, S. A.; Petkovšek, M.; Ryabenko, A. A. 4 2015 On solution spaces of products of linear differential or difference operators. Zbl 1322.68269Abramov, Sergei A.; Barkatou, Moulay A. 6 2014 Regular solutions of linear differential systems with power series coefficients. Zbl 1317.34019Abramov, S. A.; Khmelnov, D. E. 6 2014 Computable infinite power series in the role of coefficients of linear differential systems. Zbl 1416.68211Abramov, Sergei A.; Barkatou, Moulay A. 6 2014 On the dimension of solution spaces of full rank linear differential systems. Zbl 1412.34055Abramov, S. A.; Barkatou, M. A. 9 2013 Linear differential and difference systems: \(\mathrm{EG}_\delta\)- and \(\mathrm{EG}_\sigma\)-eliminations. Zbl 1311.34027Abramov, S. A.; Khmelnov, D. E. 9 2013 On singular points of solutions of linear differential systems with polynomial coefficients. Zbl 1258.34027Abramov, S. A.; Khmelnov, D. E. 12 2012 Denominators of rational solutions of linear difference systems of an arbitrary order. Zbl 1261.65134Abramov, S. A.; Khmelnov, D. E. 9 2012 On polynomial solutions of linear partial differential and \((q\)-)difference equations. Zbl 1373.68458Abramov, S. A.; Petkovšek, M. 7 2012 On valuations of meromorphic solutions of arbitrary-order linear difference systems with polynomial coefficients. Zbl 1323.68577Abramov, S. A.; Khmelnov, D. E. 2 2012 Rational solutions of linear difference equations: universal denominators and denominator bounds. Zbl 1247.65156Abramov, S. A.; Gheffar, A.; Khmelnov, D. E. 10 2011 Valuations of rational solutions of linear difference equations at irreducible polynomials. Zbl 1221.68298Gheffar, A.; Abramov, S. 9 2011 Higher-order linear differential systems with truncated coefficients. Zbl 1344.68290Abramov, S. A.; Barkatou, M. A.; Pflügel, E. 9 2011 Subanalytic solutions of linear difference equations and multidimensional hypergeometric sequences. Zbl 1232.39001Abramov, S. A.; Barkatou, M. A.; Van Hoeij, M.; Petkovšek, M. 4 2011 The research seminar on computer algebra in 2009-2010. Zbl 1242.00036Abramov, S. A.; Bogolyubskaya, A. A.; Edneral, V. F.; Rostovtsev, V. A. 3 2011 Factorization of polynomials and GCD computations for finding universal denominators. Zbl 1202.12004Abramov, S. A.; Gheffar, A.; Khmelnov, D. E. 11 2010 Polynomial ring automorphisms, rational \((w,\sigma )\)-canonical forms, and the assignment problem. Zbl 1189.33038Abramov, S. A.; Petkovšek, M. 6 2010 Indicial rational functions of linear ordinary differential equations with polynomial coefficients. Zbl 1288.34009Abramov, S. A.; Ryabenko, A. A. 1 2009 On \(m\)-interlacing solutions of linear difference equations. Zbl 1239.39001Abramov, S. A.; Barkatou, M. A.; Khmelnov, D. E. 1 2009 Dimensions of solution spaces of \(H\)-systems. Zbl 1186.33038Abramov, S. A.; Petkovšek, M. 1 2008 Analytic solutions of linear difference equations, formal series, and bottom summation. Zbl 1141.68663Abramov, S. A.; Petkovšek, M. 6 2007 An universal resolving algorithm for inverse computation of lazy languages. Zbl 1185.68328Abramov, Sergei; Glück, Robert; Klimov, Yuri 3 2007 Improved universal denominators. Zbl 1147.68877Abramov, S. A.; Polyakov, S. P. 3 2007 The research seminar on computer algebra in 2005-2006. Zbl 1137.68300Abramov, S. A.; Bogolyubskaya, A. A.; Rostovtsev, V. A.; Edneral, V. F. 2 2007 Apparent singularities of linear difference equations with polynomial coefficients. Zbl 1106.39002Abramov, S. A.; Barkatou, M. A.; van Hoeij, M. 7 2006 Solving linear systems of differential and difference equations with respect to a part of the unknowns. Zbl 1179.65100Abramov, S. A.; Bronstein, M. 7 2006 On the summation of \(P\)-recursive sequences. Zbl 1356.33011Abramov, S. A. 3 2006 In memory of Manuel Bronstein. Zbl 1208.01020Abramov, S. A. 2 2006 On regular and logarithmic solutions of ordinary linear differential systems. Zbl 1169.34301Abramov, S. A.; Bronstein, M.; Khmelnov, D. E. 10 2005 Ore polynomial rings in one variable in computer algebra. Zbl 1127.16302Abramov, S. A.; Le, H. Q.; Li, Z. 8 2005 Telescoping in the context of symbolic summation in Maple. Zbl 1137.05326Abramov, S. A.; Carette, J. J.; Geddes, K. O.; Le, H. Q. 8 2005 Gosper’s algorithm, accurate summation, and the discrete Newton-Leibniz formula. Zbl 1360.33018Abramov, S. A.; Petkovšsek, M. 5 2005 On the order of the recurrence produced by the method of creative telescoping. Zbl 1077.33037Abramov, S. A.; Le, H. Q. 1 2005 When does Zeilberger’s algorithm succeed? Zbl 1030.33011Abramov, S. A. 16 2003 The set of poles of solutions of linear difference equations with polynomial coefficients. Zbl 1076.39002Abramov, S. A.; van Hoeij, M. 3 2003 Rational canonical forms and efficient representations of hypergeometric terms. Zbl 1072.68643Abramov, S. A.; Le, H. Q.; Petkovšek, M. 2 2003 Rational normal forms and minimal decompositions of hypergeometric terms. Zbl 1005.33010Abramov, S. A.; Petkovšek, M. 18 2002 A criterion for the applicability of Zeilberger’s algorithm to rational functions. Zbl 1023.33017Abramov, S. A.; Le, H. Q. 12 2002 On the structure of multivariate hypergeometric terms. Zbl 1057.33017Abramov, S. A.; Petkovšek, M. 11 2002 Applicability of Zeilberger’s algorithm to hypergeometric terms. Zbl 1072.68642Abramov, S. A. 9 2002 Principles of inverse computation and the universal resolving algorithm. Zbl 1026.68023Abramov, Sergei; Glück, Robert 7 2002 The universal resolving algorithm and its correctness: Inverse computation in a functional language. Zbl 1014.68037Abramov, Sergei; Glück, Robert 5 2002 A direct algorithm to compute rational solutions of first order linear \(q\)-difference systems. Zbl 0995.65139Abramov, S. A. 4 2002 Computer algebra library for the construction of the minimal telescopers. Zbl 1012.68229Abramov, S. A.; Geddes, K. O.; Le, H. Q. 3 2002 On solutions of linear functional systems. Zbl 1356.65245Abramov, Sergei A.; Bronstein, Manuel 22 2001 Minimal decomposition of indefinite hypergeometric sums. Zbl 1356.33012Abramov, Sergei A.; Petkovsek, M. 7 2001 From standard to non-standard semantics by semantics modifiers. Zbl 1319.68050Abramov, Sergei; Glück, Robert 1 2001 Special formal series solutions of linear operator equations. Zbl 0972.34002Abramov, Sergei A.; Petkovšek, Marko; Ryabenko, Anna 9 2000 Applicability of Zeilberger’s algorithm to rational functions. Zbl 0963.65026Abramov, S. A.; Le, H. Q. 6 2000 Hypergeometric dispersion and the orbit problem. Zbl 1326.68340Abramov, Sergei A.; Bronstein, Manuel 5 2000 The universal resolving algorithm: Inverse computation in a functional language. Zbl 0963.68500Abramov, Sergei; Glück, Robert 5 2000 Combining semantics with non-standard interpreter hierarchies. Zbl 1044.68664Abramov, Sergei; Glück, Robert 2 2000 EG-eliminations. Zbl 0936.65144Abramov, Sergei A. 23 1999 Integration of solutions of linear functional equations. Zbl 0939.34059Abramov, Sergei A.; van Hoeij, Mark 11 1999 Rational solutions of linear difference and \(q\)-difference equations with polynomial coefficients. Zbl 0972.68184Abramov, S. A. 1 1999 \(q\)-hypergeometric solutions of \(q\)-difference equations. Zbl 0932.33019Abramov, Sergei A.; Paule, Peter; Petkovšek, Marko 29 1998 Rational solutions of first order linear difference systems. Zbl 0919.65089Abramov, S. A.; Barkatou, M. A. 22 1998 The scientific research seminar on computer algebra in 1997-1998. Zbl 0972.68814Abramov, S. A.; Rostovtsev, V. A. 3 1998 A method for the integration of solutions to Ore equations. Zbl 0919.34011Abramov, Sergei A.; van Hoeij, Mark 5 1997 Minimal completely factorable annihilators. Zbl 0929.16045Abramov, Sergei A.; Zima, Eugene 3 1997 On peripheral factorization of linear homogeneous operators. Zbl 0973.68667Abramov, S. A.; Tsarev, S. P. 1 1997 D’Alembertian solutions of inhomogeneous linear equations (differential, difference, and some other). Zbl 0966.34005Abramov, Sergei A.; Zima, Eugene V. 8 1996 On polynomial solutions of linear operator equations. Zbl 0914.65132Abramov, Sergei A.; Bronstein, Manuel; Petkovšek, Marko 25 1995 Indefinite sums of rational functions. Zbl 0914.65133Abramov, S. A. 18 1995 Rational solutions of linear difference and \(q\)-differential equations with polynomial coefficients. Zbl 0910.65107Abramov, S. A. 17 1995 Rational solutions of linear difference and \(q\)-difference equations with polynomial coefficients. Zbl 0914.65131Abramov, S. A. 11 1995 D’Alembertian solutions to linear differential and difference equations. Zbl 0919.34013Abramov, Sergei A.; Petkovšek, Marko 22 1994 The denominators of rational solutions to linear difference equations. Zbl 0824.33013Abramov, S. A. 1 1994 On the greatest common divisor of polynomials which depend on a parameter. Zbl 0925.13009Abramov, S. A.; Kvashenko, K. Yu. 3 1993 On d’Alembert substitution. Zbl 0921.34011Abramov, S. A. 1 1993 Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients. Zbl 0919.65045Abramov, S. A.; Kvansenko, K. Yu. 6 1991 An algorithm for searching quasirational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0727.65062Abramov, S. A. 1 1991 Rational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0719.65063Abramov, S. A. 29 1989 Rational solutions of linear differential and difference equations with polynomial coefficients. Zbl 0695.65051Abramov, S. A. 18 1989 Problems of computer algebra connected with the search for polynomial solutions of linear differential and difference equations. Zbl 0689.65049Abramov, S. A. 7 1989 Problems of computer algebra involved in the search for polynomial solutions of linear differential and difference equations. Zbl 0723.65048Abramov, S. A. 5 1989 The finite-difference second order equation with constant coefficients in the field of rational functions. Zbl 0369.39003Abramov, S. A. 1 1977 The rational component of the solution of a first-order linear recurrence relation with a rational right side. Zbl 0352.65062Abramov, S. A. 2 1976 Rationale Komponente der Lösung einer linearen rekurrenten Relation erster Ordnung mit rationaler rechter Seite. Zbl 0326.65069Abramov, S. A. 16 1975 On the summation of rational functions. Zbl 0255.65003Abramov, S. A. 8 1973 Über die Summation rationaler Funktionen. Zbl 0243.65076Abramov, S. A. 12 1971 all cited Publications top 5 cited Publications all top 5 Cited by 194 Authors 50 Abramov, Sergeĭ Aleksandrovich 23 Schneider, Carsten 17 Petkovšek, Marko 16 Khmelnov, Dennis E. 12 Barkatou, Moulay A. 11 Chen, Shaoshi 10 Kauers, Manuel 10 Ryabenko, Anna A. 7 Glück, Robert 7 Singer, Michael F. 7 van Hoeij, Mark 6 Blümlein, Johannes 6 Chen, William Yong-Chuan 6 Giesbrecht, Mark W. 6 Hou, Qinghu 6 Koutschan, Christoph 6 Mu, Yanping 5 Cluzeau, Thomas 5 Feng, Ruyong 5 Koepf, Wolfram A. 5 Panferov, Anton A. 4 Ablinger, Jakob 4 Bronstein, Manuel Eric 4 Gheffar, Amal 4 Labahn, George 4 Paramonov, Serge V. 4 Paule, Peter 4 Zima, Eugene V. 3 Axelsen, Holger Bock 3 Bogolyubskaya, A. A. 3 Bostan, Alin 3 Dreyfus, Thomas 3 Edneral, Victor F. 3 Garoufalidis, Stavros 3 Kotta, Ulle 3 Li, Ziming 3 Rostovtsev, Vitaly A. 3 Salvy, Bruno 3 Wang, Ronghua 3 Zeilberger, Doron 2 Chen, Vincent Y. B. 2 Cheng, Howard 2 Chyzak, Frédéric 2 Driver, Kathy A. 2 Foupouagnigni, Mama 2 Gao, Xiaoshan 2 Gu, Nancy Shan Shan 2 Halás, Miroslav 2 Hardouin, Charlotte 2 Huang, Hui 2 Kaarsgaard, Robin 2 Khavkine, Igor 2 Klein, Sebastian 2 Nishida, Naoki 2 Polyakov, S. P. 2 Prodinger, Helmut 2 Quadrat, Alban 2 Raab, Clemens G. 2 Saad, Husam L. 2 Sadykov, Timur Mradovich 2 Schost, Éric 2 Shishkina, Ol’ga Andreevna 2 Shkaravska, Olha 2 Sprenger, Torsten 2 Ulmer, Felix 2 van Eekelen, Marko 2 Vidal, Germán 2 Weideman, J. André C. 2 Weil, Jacques-Arthur 2 Yokoyama, Tetsuo 2 Zakrajšek, Helena 2 Zhang, Yi 1 Albert, Elvira 1 Alcazar, Juan Gerardo 1 Alekseeva, S. A. 1 Álvarez-Nodarse, Renato 1 Andrews, George Eyre 1 Apanovich, Marina Stepanovna 1 Arnold, John M. 1 Arreche, Carlos E. 1 Azzam, Jonas 1 Badouel, Eric 1 Baranov, M. I. 1 Bauer, Andrej 1 Beckermann, Bernhard 1 Belbachir, Hacene 1 Belikov, Juri 1 Biagioli, Riccardo 1 Böing, Harald 1 Bousquet-Mélou, Mireille 1 Brisebarre, Nicolas 1 Broughton, Gary 1 Cao, Jian 1 Carette, J. J. 1 Cattani, Eduardo H. 1 Cormier, Olivier 1 Cunha, Alcino 1 D’Andrea, Carlos 1 de Hon, Bastiaan P. 1 Dickenstein, Alicia M. ...and 94 more Authors all top 5 Cited in 60 Serials 56 Journal of Symbolic Computation 39 Programming and Computer Software 16 Advances in Applied Mathematics 7 Computational Mathematics and Mathematical Physics 5 Applicable Algebra in Engineering, Communication and Computing 5 Journal of Difference Equations and Applications 4 Discrete Mathematics 4 Theoretical Computer Science 4 Journal of Systems Science and Complexity 4 Mathematics in Computer Science 4 ACM Communications in Computer Algebra 3 Journal of Mathematical Sciences (New York) 3 The Ramanujan Journal 2 Information Processing Letters 2 Mathematics of Computation 2 Journal of Algebra 2 Journal of Computational and Applied Mathematics 2 Mathematische Annalen 2 Annals of Combinatorics 2 Higher-Order and Symbolic Computation 2 Foundations of Computational Mathematics 1 International Journal of Modern Physics A 1 Acta Informatica 1 Computer Physics Communications 1 International Journal of Control 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Prikladnaya Matematika i Mekhanika 1 Annales de l’Institut Fourier 1 Applied Mathematics and Computation 1 Duke Mathematical Journal 1 Journal of Combinatorial Theory. Series A 1 Journal of Pure and Applied Algebra 1 Kybernetika 1 Quaestiones Mathematicae 1 Cybernetics 1 Computer Aided Geometric Design 1 Journal of Complexity 1 New Generation Computing 1 Differential Geometry and its Applications 1 Designs, Codes and Cryptography 1 Linear Algebra and its Applications 1 Journal of Knot Theory and its Ramifications 1 Nuclear Physics. B. Proceedings Supplements 1 The Electronic Journal of Combinatorics 1 Integral Transforms and Special Functions 1 Communications in Contemporary Mathematics 1 Algebraic & Geometric Topology 1 The Journal of Logic and Algebraic Programming 1 Journal of Algebra and its Applications 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Frontiers of Mathematics in China 1 Journal of Physics A: Mathematical and Theoretical 1 Logical Methods in Computer Science 1 Analysis & PDE 1 Proceedings of the Estonian Academy of Sciences 1 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 1 Axioms 1 Journal of Logical and Algebraic Methods in Programming 1 Journal of Siberian Federal University. Mathematics & Physics all top 5 Cited in 40 Fields 117 Computer science (68-XX) 76 Special functions (33-XX) 51 Difference and functional equations (39-XX) 41 Field theory and polynomials (12-XX) 40 Ordinary differential equations (34-XX) 33 Numerical analysis (65-XX) 19 Combinatorics (05-XX) 15 Number theory (11-XX) 11 Commutative algebra (13-XX) 9 Quantum theory (81-XX) 7 Associative rings and algebras (16-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Partial differential equations (35-XX) 5 Operator theory (47-XX) 4 Functions of a complex variable (30-XX) 4 Sequences, series, summability (40-XX) 4 Approximations and expansions (41-XX) 4 Systems theory; control (93-XX) 3 Manifolds and cell complexes (57-XX) 2 Mathematical logic and foundations (03-XX) 2 Algebraic geometry (14-XX) 2 Category theory; homological algebra (18-XX) 2 Group theory and generalizations (20-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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