Most cited papers in Polynomial and algebraic computation
What are the most cited papers in Polynomial and algebraic computation?
The most cited paper in Polynomial and algebraic computation is "The Magma Algebra System I: The User Language" (Wieb Bosma, John Cannon, Catherine Playoust, 1997), with 7,465 citations. Next come "Matrix multiplication via arithmetic progressions" (2,313) and "Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus" (2,009).
Showing 50 of 99 papers. Every paper with more than 393 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | The Magma Algebra System I: The User Language Wieb Bosma, John Cannon, Catherine Playoust · Journal of Symbolic Computation | Sep 1997 | 7,465 |
| 2 | Matrix multiplication via arithmetic progressions Don Coppersmith, Shmuel Winograd · Journal of Symbolic Computation | Mar 1990 | 2,313 |
| 3 | Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus Stefan Hilger · Results in Mathematics | Aug 1990 | 2,009 |
| 4 | Basic Linear Algebra Subprograms for Fortran Usage Charles L. Lawson, Richard J. Hanson, David R. Kincaid et al. · ACM Transactions on Mathematical Software | Sep 1979 | 1,641 |
| 5 | Introduction to Algorithms Gerard O’Regan · Texts in computer science | 2023 | 1,630 |
| 6 | Semidefinite programming relaxations for semialgebraic problems Pablo A. Parrilo · Mathematical Programming | May 2003 | 1,600 |
| 7 | Introduction to algorithms Rudrapatna K. Shyamasundar · Resonance | Sep 1996 | 1,471 |
| 8 | A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations Peter Michael Kogge, Harold Samuel Stone · IEEE Transactions on Computers | Aug 1973 | 1,282 |
| 9 | A polyhedral branch-and-cut approach to global optimization Mohit Tawarmalani, Nikolaos V. Sahinidis · Mathematical Programming | 3 May 2005 | 1,243 |
| 10 | The Magnus expansion and some of its applications S. Blanes, F. Casas, J.A. Oteo et al. · Physics Reports | 3 Dec 2008 | 1,175 |
| 11 | Direct trajectory optimization using nonlinear programming and collocation C. HARGRAVES, Steve Paris · Journal of Guidance Control and Dynamics | Jul 1987 | 1,166 |
| 12 | A new efficient algorithm for computing Gröbner bases (F4) Jean‐Charles Faugère · Journal of Pure and Applied Algebra | Jun 1999 | 1,143 |
| 13 | Isogeometric analysis of structural vibrations J. Austin Cottrell, Alessandro Reali, Yuri Bazilevs et al. · Computer Methods in Applied Mechanics and Engineering | Mar 2006 | 1,103 |
| 14 | Isogeometric analysis using T-splines Yuri Bazilevs, Victor M. Calo, J. Austin Cottrell et al. · Computer Methods in Applied Mechanics and Engineering | 15 Mar 2009 | 1,036 |
| 15 | Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques Jean-Pierre Serre · Inventiones mathematicae | Dec 1971 | 1,006 |
| 16 | Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II Michio Jimbo, Tetsuji Miwa · Physica D Nonlinear Phenomena | Jun 1981 | 990 |
| 17 | Lagrangian Relaxation for Integer Programming Arthur M. Geoffrion | 6 Nov 2009 | 979 |
| 18 | The Umbral Calculus Steven Roman, Gian-Carlo Rota · Graduate texts in mathematics | Feb 1978 | 969 |
| 19 | On Lovász’ lattice reduction and the nearest lattice point problem László Babai · COMBINATORICA | Mar 1986 | 955 |
| 20 | PRIMES is in P Manindra Agrawal, Neeraj Kayal, Nitin Saxena · Annals of Mathematics | Sep 2004 | 936 |
| 21 | Linear Programming: Foundations and Extensions Robert J. Vanderbei · Journal of the Operational Research Society | 1998 | 915 |
| 22 | Quantifier elimination for real closed fields by cylindrical algebraic decomposition Professor Gary S. Collins · Medical Entomology and Zoology | 1975 | 899 |
| 23 | Matroids and the greedy algorithm Jack Edmonds · Mathematical Programming | Dec 1971 | 890 |
| 24 | Fundamentals of Matrix Computations. G. W. S., David S. Watkins · Mathematics of Computation | Jul 1992 | 864 |
| 25 | Solving Systems of Polynomial Equations Bernd Sturmfels · Regional conference series in mathematics | 12 Sep 2002 | 856 |
| 26 | Introduction to algorithms Giuseppe C. Calafiore, Laurent El Ghaoui · Cambridge University Press eBooks | 28 May 2018 | 824 |
| 27 | Using the generalized Schur form to solve a multivariate linear rational expectations model Paul Klein · Journal of Economic Dynamics and Control | Sep 2000 | 808 |
| 28 | A new efficient algorithm for computing Gröbner bases without reduction to zero ( F 5 ) Jean Charles Faugère | 10 Jul 2002 | 781 |
| 29 | Gröbner Bases: A Computational Approach to Commutative Algebra Thomas Becker, Volker Weispfenning, Heinz Kredel · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno | 30 Sep 2011 | 766 |
| 30 | Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations Nicolas T. Courtois, A. V. Klimov, Jacques Patarin et al. · Lecture notes in computer science | 2000 | 760 |
| 31 | A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points Hiroshi Akima · ACM Transactions on Mathematical Software | Jun 1978 | 751 |
| 32 | Polynomial interpolation in several variables Mariano Gasca, Thomas J. Sauer · Advances in Computational Mathematics | Mar 2000 | 737 |
| 33 | Self-testing/correcting with applications to numerical problems Manuel Blum, Michael G. Luby, Ronitt Rubinfeld · Journal of Computer and System Sciences | Dec 1993 | 724 |
| 34 | Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms Herbert Edelsbrunner, Ernst P. Mücke · ACM Transactions on Graphics | 3 Jan 1990 | 724 |
| 35 | Riemann's hypothesis and tests for primality Gary Lee Miller · Journal of Computer and System Sciences | Dec 1976 | 721 |
| 36 | The invariant theory of n × n matrices Claudio Procesi · Advances in Mathematics | Mar 1976 | 720 |
| 37 | Isogeometric analysis: An overview and computer implementation aspects Vinh Phu Nguyen, Cosmin Anitescu, Stéphane Bordas et al. · Mathematics and Computers in Simulation | 15 Jun 2015 | 718 |
| 38 | Interior Methods for Nonlinear Optimization Anders L. Forsgren, Philip E. Gill, Margaret H. Wright · SIAM Review | 2002 | 711 |
| 39 | Cryptanalysis of Block Ciphers with Overdefined Systems of Equations Nicolas T. Courtois, Josef Pieprzyk · Lecture notes in computer science | 2002 | 690 |
| 40 | Studies of refinement and continuity in isogeometric structural analysis J. Austin Cottrell, Thomas J.R. Hughes, Alessandro Reali · Computer Methods in Applied Mechanics and Engineering | 15 May 2007 | 672 |
| 41 | Collocation Software for Boundary-Value ODEs Uri M. Ascher, J. Christiansen, Robert D. Russell · ACM Transactions on Mathematical Software | Jun 1981 | 665 |
| 42 | Algebraic algorithms for sampling from conditional distributions Persi W. Diaconis, Bernd Sturmfels · The Annals of Statistics | Feb 1998 | 665 |
| 43 | Sums of Squares, Moment Matrices and Optimization Over Polynomials Monique Laurent · The IMA volumes in mathematics and its applications | 24 Sep 2008 | 664 |
| 44 | Rational singularities with applications to algebraic surfaces and unique factorization Joseph D. Lipman · Publications mathématiques de l IHÉS | 7 Jan 1969 | 657 |
| 45 | Direct search methods: then and now Robert Michael Lewis, Virginia J. Torczon, Michael W. Trosset · Journal of Computational and Applied Mathematics | Dec 2000 | 652 |
| 46 | Geometry of Numbers Peter M. Gruber · Birkhäuser Basel eBooks | 1979 | 649 |
| 47 | On the computational complexity and geometry of the first-order theory of the reals. Part I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals James Renegar · Journal of Symbolic Computation | Mar 1992 | 626 |
| 48 | Enumerative tropical algebraic geometry in ℝ² Grigory Mikhalkin · Journal of the American Mathematical Society | 20 Jan 2005 | 621 |
| 49 | Bruno Buchberger’s PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal Bruno Buchberger · Journal of Symbolic Computation | 16 Dec 2005 | 619 |
| 50 | Quantifier elimination for real closed fields by cylindrical algebraic decompostion George Ernest Collins · Lecture notes in computer science | 1975 | 613 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.