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See also Singular's entry in the swMATH database.

Introductory Textbooks

  1. Wolfram Decker, Gerhard Pfister: A First Course in Computational Algebraic Geometry
    Cambridge University Press, 2013.
  2. Wolfram Decker, Christoph Lossen: Computing in Algebraic Geometry - A Quick Start using Singular
    Springer Verlag, 2005, ACM 16.
  3. Gert-Martin Greuel, Gerhard Pfister: A Singular Introduction to Commutative Algebra
    Springer Verlag, with contributions by Olaf Bachmann, Christoph Lossen, and Hans Schönemann, 2002, Second edition appeared in 2007.

Overview Articles

  1. Gert-Martin Greuel, Gerhard Pfister: Singular and Applications
    Jahresbericht der DMV, 108, 167-196, 2006.
  2. Christoph Lossen, Hans Schönemann: 21 years of Singular experiments in mathematics
    In: C. Lossen, G. Pfister: Singularities and Computer Algebra, Cambridge University Press, 247-272, 2006.
  3. Christoph Lossen: Singular: A Computer Algebra System
    CISE, 5 (4), 45-55, 2003.
  4. Gert-Martin Greuel, Gerhard Pfister, Hans Schönemann: Singular - A Computer Algebra System for Polynomial Computations
    In: M. Kerber and M. Kohlhase (eds.), Symbolic Computation and Automated Reasoning, The Calculemus-2000 Symposium, 227-233, 2001.
  5. Gert-Martin Greuel: Applications of Computer Algebra to Algebraic Geometry, Singularity Theory and Symbolic-Numerical Solving
    In: European Congeress of Mathematicians, Barcelona, July 10-14, 2000, 2, 169-188, 2000.
  6. Gert-Martin Greuel: Computer Algebra and Algebraic Geometry - Achievements and Perspectives
    Journal of Symbolic Computation, 30 (3), 253-290, 2000.
  7. Gert-Martin Greuel, Gerhard Pfister: Gröbner bases and algebraic geometry
    In: B. Buchberger and F. Winkler: Gröbner Bases and Applications. LNS, 251, 109-143, 1998.
  8. Gert-Martin Greuel: Description of Singular: A Computer Algebra System for Singularity Theory, Algebraic Geometry and Commutative Algebra
    Euromath Bulletin, 2, 161-172, 1996.

Manual, Tutorial and Reference Card for Singular

  1. Singular Manual: for latest version (PDF, HTML).
  2. Singular Manual: for Version 2 (HTML).
  3. Reference Card: Pdf.

Singular Presentations

  1. Anne Frühbis-Krüger, Andreas Steenpass, Stefan Steidel: Singular 3-1-3 - Tackling New Challenges
    MEGA Conference, Stockholm, Sweden, 2011.
  2. Stefan Steidel: Singular Tutorial
    Summer School in Trieste, 2008.
  3. Gerhard Pfister: Presentation of new Implemented Algorithms
    MEGA Conference, Kaiserslautern, Germany, 2003.
  4. Anne Frühbis-Krüger, Christoph Lossen: Singular as a tool for Singularity Theory
    7th Workshop on Real and Complex Singularities, ICMC-USP, Sao Carlos, Brazil, 2002.
  5. Hans Schönemann: The system Singular
    ISSAC, Lille, France, 2002.
  6. Anne Frühbis-Krüger: A Computer Algebra System for Polynomial Computations
    Mathematical Institute of Paris 6/7, 2001.
  7. Gert-Martin Greuel: New Developments in Singularity Theory
    Summer School New Developments in Singularity Theory in Cambridge, UK, 2000.
  8. Gert-Martin Greuel, Gerhard Pfister: System und Anwendungen
    DFG Tagung Effiziente Algorithmen, Karlsruhe, Germany, 2000.
  9. Christoph Lossen: Singular presentation
    Aspectos Computacionales en Álgebra Conmutativa y Geometría Algebraica, Valladolid, Spain, 2000.
  10. Gert-Martin Greuel, Gerhard Pfister, Hans Schönemann: Singular presentation
    DMV Tagung, Mainz, Germany, 1999.
  11. Olaf Bachmann, Hans Schönemann: Monomial Representations for Groebner Bases Computations
    ISSAC, Rostock, Germany, 1998.
  12. Gert-Martin Greuel, Gerhard Pfister, Hans Schönemann: A Computer Algebra System for Polynomial Computations
    ICM, Berlin, Germany, 1998.
  13. Gert-Martin Greuel, Gerhard Pfister, Hans Schönemann: Singular version 1.2 -- What is new ?!
    MEGA Conference, Saint Malo, France, 1998.

Information on Implemented Algorithms and Libraries

  1. Burcin Erocal, Oleksandr Motsak, Frank-Olaf Schreyer, Andreas Steenpass: Refined Algorithms to Compute Syzygies
    J. Symb. Comput., 74, 308-327, 2016.
  2. Magdaleen S. Marais, Andreas Steenpass: The Classification of Real Singularities Using SINGULAR. Part II: The Structure of the Equivalence Classes of the Unimodal Singularities
    J. Symb. Comput., 74, 346-366, 2016.
  3. Janko Boehm, Magdaleen S. Marais, Andreas Steenpass: The Classification of Real Singularities Using Singular. Part III: Unimodal Singularities of Corank 2
    Preprint, 2015.
  4. Dereje Kifle Boku, Wolfram Decker, Claus Fieker, Andreas Steenpass: Gröbner Bases over Algebraic Number Fields
    PASCO '15 Proceedings of the 2015 International Workshop on Parallel Symbolic Computation, Bath, 16-24, 2015.
  5. Magdaleen S. Marais, Andreas Steenpass: The Classification of Real Singularities Using SINGULAR. Part I: Splitting Lemma and Simple Singularities
    J. Symb. Comput., 68, 61-71, 2015.
  6. Janko Boehm, Kathrin Bringmann, Arne Buchholz, Hannah Markwig: Tropical mirror symmetry for elliptic curves
    arXiv:1309.5893, 2013.
  7. Janko Boehm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister, Andreas Steenpass, Stefan Steidel: Parallel algorithms for normalization
    J. Symb. Comput., 51, 99-114, 2013.
  8. Muhammad Ahsan Banyamin, Gerhard Pfister, Stefan Steidel: About the computation of the signature of surface singularities z^N+g(x,y)=0
    Central European Journal of Mathematics, 10(1), 271-276, 2012.
  9. Janko Boehm, Wolfram Decker, Claus Fieker, Gerhard Pfister: The use of Bad Primes in Rational Reconstruction
    arXiv:1207.1651, 2012.
  10. Christian Eder: Improving incremental signature-based Groebner basis algorithms
    submitted to ISSAC 2012, 2012.
  11. Calin-Serban Barbat: Dualization of projective algebraic sets by using Gröbner bases elimination techniques
    arXiv:1101.2615, 2011.
  12. Nazeran Idrees, Gerhard Pfister, Stefan Steidel: Parallelization of Modular Algorithms
    Journal of Symbolic Computation, 46, 672-684, 2011.
  13. Michael Monagan, Roman Pearce: Sparse polynomial division using a heap
    Journal of Symbolic Computation, 46 (7), 807-822, 2011.
  14. Gerhard Pfister, Afshan Sadiq, Stefan Steidel: An Algorithm for Primary Decomposition in Polynomial Rings over the Integers
    Central European Journal of Mathematics, 9(4), 897-904, 2011.
  15. Gert-Martin Greuel, Santiago Laplagne, Frank Seelisch: Normalization of rings
    Journal of Symbolic Computation, 45 (9), 887-952, 2010.
  16. Martin Monerjan: An Algorithm to Compute the Gröbner Fan of a Polynomial Ideal and its Implementation into SINGULAR
    Universität Kaiserslautern, 2010, Diplomarbeit.
  17. Michael Brickenstein, Alexander Dreyer : PolyBoRi: A framework for Groebner-basis computations with Boolean polynomials
    Journal of Symbolic Computation, 44 (9), 1326-1345, 2009.
  18. Anders Nedergaard Jensen, Hannah Markwig, Thomas Markwig: An algorithm for lifting points in a tropical variety
    Collectanea Mathematica, 59 (2), 129-165, 2008.
  19. Anne Frühbis-Krüger, Gerhard Pfister: Algorithmic Resolution of Singularities
    Lecture Notes of LMS, Cambridge University Press, 2006.
  20. Michael Brickenstein : Slimgb: Gröbner bases with slim polynomials
    Reports on Computer Algebra (ZCA, University of Kaiserslautern), 35, 2005.
  21. Tobias Hirsch: Computing the Integral Closure of an Ideal Using its Rees Algebra
    Computational Commutative and Non-Commutative Algebraic Geometry (IOS Press), 196, 145-155, 2005.
  22. Viktor Levandovskyy : Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation
    PhD Thesis (University of Kaiserslautern), 2005.
  23. Mathias Schulze : Good bases for tame polynomials
    Journal of Symbolic Computation, 39 (1), 103-126, 2005.
  24. E. A. Tobis : Libraries for Counting Real Roots
    Reports on Computer Algebra (ZCA, University of Kaiserslautern), 34, 2005.
  25. Anne Frühbis-Krüger, Gerhard Pfister: Practical Aspects of Algorithmic Resolution of Singularities
    Reports on Computer Algebra (ZCA, University of Kaiserslautern), 33, 2004.
  26. Mathias Schulze : A normal form algorithm for the Brieskorn lattice
    Journal of Symbolic Computation, 38 (4), 1207-1225, 2004.
  27. Anne Frühbis-Krüger, Kai Krüger, Hans Schönemann: Dynamic Modules in Singular
    Reports on Computer Algebra (ZCA, University of Kaiserslautern), 32, 2003.
  28. Viktor Levandovskyy : PBW Bases, Non-Degeneracy Conditions and Applications
    Proc. of the ICRA X conference, Toronto, Canada. Fields Institute, 2003.
  29. Viktor Levandovskyy, Hans Schönemann: PLURAL - a Computer Algebra System for Noncommutative Polynomial Algebras
    Proc. of the ISSAC 2003, Philadelphia, USA, 2003.
  30. I Made Sulandra: Über Gröbnerwalkalgorithmen
    PhD Thesis (Universität des Saarlandes), 2003.
  31. F. Hernando : Computation of the Alexander polynomial of a plane curve singularity and an implementation in Singular
    Master Thesis (University of Kaiserslautern), 2002.
  32. Viktor Levandovskyy : On Gröbner bases for noncommutative G-algebras
    Proc. of the 8th Rhine Workshop on Computer Algebra, Mannheim, Germany, 2002.
  33. Chris Monico: Computing the primary decomposition of zero-dimensional ideals
    Journal of Symbolic Computation, 34 (5), 451-459, 2002.
  34. Hans Schönemann: Data representations in the computer algebra system Singular
    Workshop on Applications of Commutative Algebra, Catania, 2002.
  35. Mathias Schulze : The differential structure of the Brieskorn lattice
    A. M. Cohen et al.: Mathematical Software - ICMS 2002, World Scientific, 136-146, 2002.
  36. Mathias Schulze : Algorithmic Gauss-Manin Connection
    PhD Thesis (University of Kaiserslautern), 2002.
  37. Vladimir P. Gerdt, Yuri A. Blinkov, Denis A. Yanovich : Construction of Janet bases I: Monomial bases
    E. Ghanza et al (eds.), Computer Algebra in Scientific Computing - CASC 2001. (Springer), 233-247, 2001.
  38. Vladimir P. Gerdt, Yuri A. Blinkov, Denis A. Yanovich : Construction of Janet bases II: Polynomial bases
    E. Ghanza et al (eds.), Computer Algebra in Scientific Computing - CASC 2001. (Springer), 249-263, 2001.
  39. Gert-Martin Greuel, Christoph Lossen, Mathias Schulze: Three Algorithms in Algebraic Geometry, Coding Theory and Singularity Theory
    C. Ciliberto et al: Application of Algebraic Geometry to Coding Theory, Physics and Computation, Proceedings. (Kluwer), 161-194, 2001.
  40. Mathias Schulze : Algorithms for the Gauss-Manin connection
    Journal of Symbolic Computation, 32 (5), 549-564, 2001.
  41. Mathias Schulze, Joseph H. M. Steenbrink : Computing Hodge-theoretic invariants of singularities
    D. Siersma et al.: New Developments in Singularity Theory. NATO Science Series (Kluwer), 21, 217-233, 2001.
  42. Thomas Bayer : Computation of moduli spaces for semiquasihomogenous singularities and an implementation in Singular
    Diploma Thesis (University of Kaiserslautern), 2000.
  43. T. Siebert : Recursive Computation of Free Resolutions and a Generalized Koszul Complex
    Reports on Computer Algebra (ZCA, University of Kaiserslautern), 28, 2000.
  44. Agnes Eileen Heydtmann: Generating Invariant Rings of Finite Groups
    Diploma Thesis (Universität des Saarlandes), 1999.
  45. Dietmar Hillebrand : Triangulierung nulldimensionaler Ideale - Implementierung und Vergleich zweier Algorithmen
    Diploma Thesis (Universität Dortmund), 1999.
  46. Martin Lamm : Hamburger-Noether Entwicklung von Kurvensingularitäten
    Diploma Thesis (University of Kaiserslautern), 1999.
  47. Hans Schönemann : Polynomials in Factory and Singular
    Nikolaus-Konferenz Aachen, 1999.
  48. Mathias Schulze : Computation of the Monodromy of an Isolated Hypersurface Singularity
    Diploma Thesis (University of Kaiserslautern), 1999.
  49. Christine Theis : Der Buchberger-Algorithmus für torische Ideale und seine Anwendung in der ganzzahligen Optimierung
    Diploma Thesis (Universität des Saarlandes), 1999.
  50. Moritz Wenk : Resultantenmethoden zur Lösung algebraischer Gleichungssysteme implementiert in Singular
    Diploma Thesis (University of Kaiserslautern), 1999.
  51. O. Bachmann, Hans Schönemann : Monomial Representations for Groebner Basis Computations
    Reports on Computer Algebra (ZCA, University of Kaiserslautern), 18, 1998.
  52. Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister: Primary decomposition: algorithms and comparisons
    Gert-Martin Greuel, B. H. Matzat, G. Hiss: Algorithmic Algebra and Number Theory (Springer), 187-220, 1998.
  53. Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister, Theo de Jong: The normalisation: a new algorithm, implementation and comparisons
    Proc. EUROCONFERENCE Computational Methods for Representations of Groups and Algebras 1997, 1998.
  54. Wolfram Decker, Agnes Eileen Heydtmann, Frank-Olaf Schreyer : Generating a Noetherian Normalization of the Invariant Ring of a Finite Group
    Journal of Symbolic computation, 25 (6), 727-731, 1998.
  55. Wolfram Decker, Theo de Jong : Gröbner bases and invariant theory
    Gröbner bases and applications, London Math. Soc. Lecture Notes Series, 251, 61-89, 1998.
  56. Bernd Martin : Computing versal deformations with singular
    G.-M. Greuel, B. H. Matzat, G. Hiss: Algorithmic Algebra and Number Theory (Springer), 283-294, 1998.
  57. O. Bachmann, S. Gray, Hans Schönemann : MP Prototype Specification
    Reports on Computer Algebra (ZCA, University of Kaiserslautern), 12, 1997.
  58. Kai Krüger: Klassifikation von Hyperflächensingularitäten
    Diploma Thesis (University of Kaiserslautern), 1997.
  59. Tim Wichmann : Der FGLM Algorithmus - verallgemeinert und implementiert in Singular
    Diploma Thesis (University of Kaiserslautern), 1997.
  60. Olaf Bachmann, Simon Gray, Hans Schönemann: MPP: a framework for distributed polynomial computations
    Proc. of the ISSAC, Zurich, Switzerland, 103-112, 1996.
  61. H. Grassmann, Gert-Martin Greuel, Bernd Martin, W. Neumann, Gerhard Pfister, Pohl Wilfred, Hans Schönemann, T. Siebert: On an implementation of standard bases and syzygies in Singular
    AAECC 7, 235-149, 1996.
  62. Gert-Martin Greuel, Gerhard Pfister: Advances and improvements in the theory of standard bases and syzygies
    Archiv der Mathematik (Birkhäuser), 66 (2), 163-176, 1996.
  63. Hans Schönemann : Algorithms in Singular
    Reports on Computer Algebra (ZCA, University of Kaiserslautern), 2, 1996.
  64. T. Siebert : On strategies and implementations for computations of free resolutions
    Reports on Computer Algebra (ZCA, University of Kaiserslautern), 8, 1996.
  65. H. Grassmann, Gert-Martin Greuel, Bernd Martin, W. Neumann, Gerhard Pfister, Pohl Wilfred, Hans Schönemann, T. Siebert: Standard bases, syzygies and their implementation in Singular
    Beiträge zur angewandten Analysis und Informatik. Shaker, Aachen, 69-96, 1994.

Further Books providing Singular Examples

  1. Teijo Arponen, Andreas Mueller, Samuli Piipponen, Jukka Tuomela: Kinematical analysis of overconstrained and underconstrained mechanisms by means of computational algebraic geometry
    Meccanica (Springer), 49, 843-862, 2014.
  2. Teijo Arponen, Andreas Mueller, Samuli Piipponen, Jukka Tuomela: Computational algebraic geometry and global analysis of regional manipulators
    Applied Mathematics and Computation, 232, 820-835, 2014.
  3. Timo Erkama, Samuli Piipponen: Rational Cycles of Quadratic Polynomials
    JP Journal of Algebra, Number Theory and Applications, 33, 113-132, 2014.
  4. Teijo Arponen, Samuli Piipponen, Jukka Tuomela: Classification of Singularities in Kinematics of Mechanisms
    Mechanisms and Machine Science, 15, 41-48, 2013.
  5. Samuli Piipponen, Jukka Tuomela: Algebraic analysis of kinematics of multibody systems
    Mechanical Sciences, 4, 33-47, 2013.
  6. Samuli Piipponen, Jukka Tuomela: Configuration space analysis of rigid mechanisms
    Miskolc Mathematical Notes , 14, 685-695, 2013.
  7. Viktor Levandovskyy, Jorge Martín-Morales: Algorithms for checking rational roots of b-functions and their applications
    Journal of Algebra, 352, 408-429, 2012.
  8. Iwona Krzyżanowska: The intersection number of real polynomial mappings
    Topology and its Applications, 158, 379-386, 2011, issue 3.
  9. Iwona Karolkiewicz, Aleksandra Nowel, Zbigniew Szafraniec: An algebraic formula for the intersection number of a polynomial immersion
    J. Pure Appl. Algebra, 214, 269–280, 2010, no. 3.
  10. Anne Frühbis-Krüger: Some Remarks on Blowing-Ups in a Computer Algebra System
    Computer Science Journal of Moldova, 16, 15--34, 2008.
  11. Valery Romanovski, Douglas Shafer: The Center and Cyclicity Problems. A Computational Algebra Approach
    Birkhäuser, 2008.
  12. Frühbis-Krüger Anne: Computational Aspects of Singularities
    in Singularities in Geometry and Topology, World Scientific Publishing, 253--327, 2007, only older and shorter version available online.
  13. Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin: Introduction to Singularities and Deformations
    Springer Monographs in Mathematics, 2007.
  14. Bernd Sturmfels: Solving Systems of Polynomial Equations
    CBMS Regional Conference Series in Mathematics, AMS, Providence, 97, 2002.
  15. David A. Cox, John B. Little, Donal O'Shea: Using Algebraic Geometry
    Springer Verlag, 1998.
  16. David A. Cox, John B. Little, Donal O'Shea: Ideals, Varieties, and Algorithms
    Springer Verlag, 1997.

Further Publications Referring to Singular

  1. Thorsten Theobald: An enumerative geometry framework for algorithmic line problems in R^3
    SIAM Journal on Computing, 31 (4), 1212-1228, SIAM.
  2. Olav Geil, Ryutaroh Matsumoto, Diego Ruano: List Decoding Algorithm based on Voting in Gröbner Bases for General One-Point AG Codes
    Journal of Symbolic Computation, published online, 2016.
  3. Hagai Kirshner, Michael Unser, John Paul Ward: On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data
    IEEE TRANSACTIONS ON SIGNAL PROCESSING, 62, 1361 -- 1376, 2014.
  4. Teijo Arponen, Samuli Piipponen, Jukka Tuomela: Kinematical analysis of Wunderlich mechanism
    Mechanism and Machine Theory, 70, 16-31, 2013.
  5. Hiep Dang: Computations in multivariate quaternionic polynomial ring
    Le Matematiche, LXVIII, 3-11, 2013.
  6. Marcin Dumnicki, Tomasz Szemberg, Halszka Tutaj-Gasinska: A counter-example to a question by Huneke and Harbourne
    2013, arXiv:1301.7440.
  7. Akihito Kikuchi: An approach to first principles electronic structure calculation by symbolic-numeric computation
    Qscience connect , Bloomsbury Qatar Foundation Journals, 2013, No.1, 2013.
  8. Federico Ardila, Megan Owen, Seth Sullivant: Geodesics in CAT(0) cubical complexes
    Advances in Applied Mathematics, 48 (1), 142-163, 2012.
  9. G. Dibitetto, A. Guarino, D. Roest: Vacua analysis in extended supersymmetry compactifications
    Progress of Physics, 60 (3), 2012.
  10. Amir Hashemi: Efficient computation of Castelnuovo-Mumford regularity
    Mathematics of Computation, 81, 1163-1177, 2012.
  11. Nathan Owen Ilten, Lars Kastner: Calculating Generators of Multigraded Algebras
    2012.
  12. Akihito Kikuchi: A proposal to first principles electronic structure calculation:Symbolic-Numeric method
    preprint, 2012, 42.
  13. David J. Marchette: Minimal Free Resolutions of Graph Edge Ideals
    2012.
  14. Bernd Martin, Dmitry Pochekutov: Discriminant and Singularities of Logarithmic Gauss Map, Examples and Application
    2012.
  15. Jeaman Ahn, Sijong Kwak, YeongSeok Song: Generic Initial ideals of Singular Curves in Graded Lexicographic Order
    2011.
  16. D.G. Aliaga, M. Boutin, Ji Zhang: Pose-Free Structure From Motion Using Depth From Motion Constraints
    IEEE Transactions on Image Processing, 20 (10), 2937-2953, 2011.
  17. Elizabeth S. Allman, James H. Degnan, John A. Rhodes: Identifying the Rooted Species Tree from the Distribution of Unrooted Gene Trees under the Coalescent
    Journal of Mathematical Biology, 62 (6), 833-862, 2011.
  18. Gwénolé Ars, Amir Hashemi: Computing Syzygies by Faugère's F_5 Algorithm
    Results in Mathematics, 59 (1-2), 35-42, 2011.
  19. Daniel J. Bates, Luke Oeding: Toward a salmon conjecture
    Experimental Mathematics, 20 (3), 358–370, 2011.
  20. Srinivas Behara, Shiv Datt Kumar, Ratnesh Kumar Mishra: On Projective Modules and Computation of Dimension of a Module over Laurent Polynomial Ring
    ISRN Algebra, 2011, 12, 2011.
  21. Janko Boehm, David Eisenbud, Max Nitsche: Decomposition of semigroup algebras
    to appear in Experimental Mathematics, 2011.
  22. Gary Carter, Ed Dawson, Huseyin Hisil, Kenneth Koon-Ho Wong: An exploration of affine group laws for elliptic curves
    Journal of Mathematical Cryptology, 5 (1), 1-50, 2011.
  23. Víctor Castellanos, Abel Castorena, Manuel Cruz-López: Algebraic and Computational Formulas for the Index of Real Analytic Vector Fields
    Results in Mathematics, 59 (1-2), 125-139, 2011.
  24. Sandra Di Rocco, David Eklund, Chris Peterson, Andrew J. Sommese: Chern Numbers of Smooth Varieties via Homotopy Continuation and Intersection Theory
    Journal of Symbolic Computation, 46 (1), 23-33, 2011.
  25. Christian Eder, John Perry: Signature-based algorithms to compute Groebner bases
    submitted to ISSAC 2011, 16 pages, 2011.
  26. Graham Ellis, Paul Smith: Computing group cohomology rings from the Lyndon-Hochschild-Serre spectral sequence
    Journal of Symbolic Computation, 46 (4), 360-370, 2011.
  27. F. Enescu, Lv Jinpeng, P. Kalla: Verification of composite Galois field multipliers over GF((2^m)^n) using computer algebra techniques
    High Level Design Validation and Test Workshop (HLDVT), 2011 IEEE International, 2011, 136-143, 2011.
  28. Raul M. Falcón: The set of autotopisms of partial Latin squares
    arXiv:1107.3248v1 [math.CO], 2011.
  29. David J. Green, Simon King: The computation of the cohomology rings of all groups of order 128
    Journal of Algebra, 325, 352-363, 2011.
  30. Kenji Hashimoto, Tomohide Terasoma: Period map of a certain K3 family with an S5-action
    Journal für die reine und Angewandte Mathematik, 2011 (652), 1-65, 2011.
  31. Dang Tuan Hiep: Computing Serre\'s Intersection Multiplicities
    2011.
  32. Franziska Hinkelmann, Abdul Salam Jarrah, Reinhard Laubenbacher, David Murrugarra: A Mathematical Framework for Agent Based Models of Complex Biological Networks
    Bulletin of Mathematical Biology, 73 (7), 1583-1602, 2011.
  33. Shutaro Inoue, Katsusuke Nabeshima, Ko Sakai, Yosuke Sato, Akira Suzuki: Boolean Gröbner bases
    Journal of Symbolic Computation, 46 (5), 622-632, 2011.
  34. Sebastian Jambor: Computing minimal associated primes in polynomial rings over the integers
    Journal of Symbolic Computation, 46 (10), 1098-1104, 2011.
  35. Taro Kawazoe, Masayuki Noro: Algorithms for computing a primary ideal decomposition without producing intermediate redundant components
    Journal of Symbolic Computation, 46 (10), 1158–1172, 2011.
  36. Iwona Krzyżanowska, Zbigniew Szafraniec: Polynomial mappings into a Stiefel manifold and immersions
    2011.
  37. Margreta Kuijper, Kristina Schindelar: Minimal Gröbner bases and the predictable leading monomial property
    Linear Algebra and its Applications, 434 (1), 104-116, 2011.
  38. Zbigniew Leśniak Leśniak, Yong-Guo Shi: One class of planar rational involutions
    Nonlinear Analysis: Theory, Methods & Applications, 74 (17), 6097-6104, 2011.
  39. Viktor Levandovskyy, Kristina Schindelar: Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases
    Journal of Symbolic Computation, 46 (5), 595-608, 2011.
  40. Ulrich Loup, Erika Ábrahám: GiNaCRA: A C++ Library for Real Algebraic Computations
    Lecture Notes in Computer Science, 6617, 512-517, 2011.
  41. Agustin Marcelo, Peter Schenzel: Non-Cohen-Macaulay unique factorization domains in small dimensions
    Journal of Symbolic Computation, 46 (5), 609-621, 2011.
  42. Dhagash Mehta: Numerical Polynomial Homotopy Continuation Method and String Vacua
    Advances in High Energy Physics, 2011, 15, 2011.
  43. Dorin Popescu: Depth of factors of square free monomial ideals
    2011.
  44. Johannes Rauh: Finding the Maximizers of the Information Divergence from an Exponential Family
    IEEE Transactions on Information Theory, 57 (6), 3236-3247, 2011.
  45. Elizabeth A. Sell: On splice quotients of the form {z^n = f(x,y)}
    Mathematische Nachrichten, 284 (10), 1286-1303, 2011.
  46. Yi-Huang Shen: Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three
    Communications in Algebra, 39 (5), 1922-1940, 2011.
  47. Beata Strycharz-Szemberg, Tomasz Szemberg: Geometry of the locus of polynomials of degree 4 with iterative roots
    Central European Journal of Mathematics, 9 (2), 338-345, 2011.
  48. Melle-Hernandez Alejandro, Arta-Bartolo Enrique, Luengo Ignacio, Fernandez de Bobadilla Javier: Milnor number of weighted-Le-Yomdin singularities
    Int. Math. Res. Not., 22, 4301-4318, 2010.
  49. Jinpeng An, Dragomir Ž. Đoković: Zero patterns and unitary similarity
    Journal of Algebra, 324 (1), 51-80, 2010.
  50. Jingeng An, Dragomir Z. Dokovic: Zero Patterns and Unitary Similarity
    Journal of Algebra, 324 (1), 51-80, 2010.
  51. Lara B. Anderson, James Gray, Dan Grayson, Yang-Hui He, André Lukas: Yukawa Couplings in Heterotic Compactification
    Communications in Mathematical Physics, 297 (1), 95-127, 2010.
  52. Daniel Andres, Viktor Levandovskyy, Jorge Martin-Morales: Effective Methods for the Computation of Bernstein-Sato polynomial for Hypersurfaces and Affine Varieties
    2010.
  53. Rémi Arcadias: Multidegree for bifiltered D-modules
    2010.
  54. Mohamed Barakat, Markus Lange-Hegermann : An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization
    JPAA, 2010.
  55. Tanja Becker: On the existence of symplectic resolutions of symplectic reductions
    Mathematische Zeitschrift, 265 (2), 343-363, 2010.
  56. Christine Berkesch, Anton Leykin: Algorithms for Bernstein-Sato polynomials and multiplier ideals
    2010.
  57. Cinzia Bisi, Francesco Polizzi: On Proper Polynomial Maps of C^2
    Journal of Geometric Analysis, 20, 72-89, 2010.
  58. Yousra Boubakri, Gert-Martin Greuel, Thomas Markwig: Invariants of Hypersurface Singularities in Positive Characteristic
    2010.
  59. Volker Braun : Three generations on the quintic quotient
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  60. Michael Brickenstein, Stanislav Bulygin : Obtaining and solving systems of equations in key variables only for the small variants of AES
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  61. Andries E. Brouwer, Mihaela Popoviciu : The invariants of the binary nonic
    Journal of Symbolic Computation, 45 (6), 709-720, 2010.
  62. Johannes Buchmann, Stanislav Bulygin, Albrecht Petzoldt: Selecting Parameters for the Rainbow Signature Scheme
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  63. Stanislav Bulygin, Ruud Pellikaan : Decoding and finding the minimum distance with Gröbner bases: history and new insights
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  65. Aldo Conca, Tim Römer: Generic initial ideals and fibre products
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  67. Alberto Damiano, Graziano Gentili, Daniele Struppa: Computations in the ring of quaternionic polynomials
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  68. Ruchira S. Datta : Finding all Nash equilibria of a finite game using polynomial algebra
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  69. Alicia Dickenstein, Laura Felicia Matusevich, Ezra Miller: Combinatorics of binomial primary decomposition
    Mathematische Zeitschrift, 264 (4), 745-763, 2010.
  70. Christian Eder, Justin Gash, John Perry: Modifying Faugère's F5 Algorithm to ensure termination
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  76. Carlos Galindo, Francisco Monserrat: On the Characterization of Algebraically Integrable Plane Foliations
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  77. Jaume Giné, Valery G. Romanovski: Integrability conditions for Lotka–Volterra planar complex quintic systems
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  78. Gert-Martin Greuel, Frank Seelisch, Oliver Wienand: The Groebner basis of the ideal of vanishing polynomials
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  79. Eleonora Guerrini, Emmanuela Orsini, Massimiliano Sala: Computing the distance distribution of systematic nonlinear codes
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  80. Amina Hadj Kacem, Ihsen Yengui: Dynamical Gröbner bases over Dedekind rings
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  81. Maoan Han, Valery G. Romanovski: Estimating the number of limit cycles in polynomials systems
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  82. Franziska Hinkelmann, Reinhard Laubenbacher, David Murrugarra, Abdul Salam Jarrah: A Mathematical Framework for Agent Based Models of Complex Biological Networks
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  83. Hans Jockers, Peter Mayr, Johannes Walcher: On N=1 4d Effective Couplings for F-theory and Heterotic Vacua
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  87. Dmitry Kerner: On some generalizations of Newton non-degeneracy for hypersurface singularities
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  88. Johanna Knapp, Emanuel Scheidegger: Matrix factorizations, Massey products and F-terms for two-parameter Calabi-Yau hypersurfaces
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  106. Ibrahim Al-Ayyoub: Normality of Monomial Ideals
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  120. Rocio Blanco: Complexity of Villamayor's algorithm in the non-exceptional monomial case
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  121. M. Borges-Quintana, M.A. Borges-Trenard, E. Martinez-Moro : An Application of Möller's Algorithm to Coding Theory
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  122. Yousra Boubakri: Hypersurface singularities in positive characteristic
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  128. Stanislav Bulygin, Ruud Pellikaan : Decoding linear error-correcting codes up to half the minimum distance with Gröbner bases
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    Tokyo Journal of Mathematics, 27 (1), 239-253, 2004.
  402. Shun-Ichiro Okuda: Kernels of derivations in positive characteristic
    Hiroshima Mathematical Journal, 34 (1), 1-19, 2004.
  403. Hyungju Park: Symbolic computation and signal processing
    Journal of Symbolic Computation, 37 (2), 209-226, 2004.
  404. Wiland Schmale, Pramod K. Sharma: Cyclizable matrix pairs over C[x] and a conjecture on Töplitz pencils
    Linear Algebra and its Applications, 389 (1), 33-42, 2004.
  405. Shustin Shustin, Eric Westenberger: Projective hypersurfaces with many singularities of prescribed types
    Journal of the LMS, 70 (3), 609-624, 2004.
  406. Jan Stevens : Some adjacencies to cusp singularities
    Real and Complex Singularities. Contemporary Mathematics, Amer. Math. Soc., 354, 291-300, 2004.
  407. Irena Swanson: On the embedded primes of the Mayr-Meyer ideals
    Journal of Algebra, 275 (1), 143-190, 2004.
  408. Johannes Zimmer: Stored energy functions for phase transitions in crystals
    Archive for Rational Mechanics and Analysis, 172 (2), 191-212, 2004.
  409. Francois Anton, Darka Mioc: A certified predicate for maintaining the topology of the Voronoi diagram for conics
    Proc. X Encuentros de Geometria Computacional, 2003.
  410. Thomas Bayer: An Algorithm for Computing Invariants of Linear Actions of Algebraic Groups up to a given Degree
    Journal of Symbolic Computation, 35 (4), 441-449, 2003.
  411. Thomas Bayer: Algorithms for the Computation of Moduli Spaces for Semiquasihomogeneous Singularities
    Revista Matemática Complutense , 16 (1), 103-129, 2003.
  412. Markus Brodmann, Peter Schenzel: On projective curves of maximal regularity
    Mathematische Zeitschrift, 244 (2), 271-289, 2003.
  413. Winfried Bruns, Wolmer V. Vasconcelos: Minors of symmetric and exterior powers
    Journal of Pure and Applied Algebra, 179 (3), 235-240, 2003.
  414. Igor Burban, Hans-Georg Freiermuth : Geometrical properties of sections of Buchsbaum-Rim sheaves
    2003.
  415. Massimo Caboara, C. Traverso: Efficient algorithms for basic module operations
    2003.
  416. Arthur D. Chtcherba : A new Sylvester-type Resultant Method based on the Dixon-Bzout Formulation
    2003.
  417. A. Collino, Stefan Müller-Stach, Shuji Saito: On K1 and K2 of algebraic surfaces
    K-Theory, 30 (1), 37-69, 2003.
  418. Nicolas T. Courtois, Magnus Daum, Patrick Felke : On the Security of HFE, HFEv- and Quartz
    Lecture Notes in Computer Science, 2567, 337-350, 2003.
  419. James Damon: On the Legacy of Free Divisors II: Free* Divisors and Complete Intersections
    Moscow Mathematical Journal, 3 (2), 361-395, 2003.
  420. Ruchira S. Datta : Using computer algebra to find Nash equilibria
    Proc. of the ISSAC, 74-79, 2003.
  421. Viviana Ene, Dorin Popescu : Rank one Maximal Cohen-Macaulay modules over singularities of type Y_1^3+Y_2^3+Y_3^3+Y_4^3
    2003.
  422. Gert-Martin Greuel: A Computer Algebra Solution to a Problem in Finite groups
    Revista Matematica Iberoamericana, 19 (2), 413-424, 2003.
  423. Agnes Eileen Heydtmann: Sudan-decoding generalized geometric Goppa codes
    Finite Fields and Their Applications, 9 (3), 267-285, 2003.
  424. V. H. Jorge Pérez: Polar multiplicities and equisingularity of map germs from C^3 to C^3
    Houston Journal of Mathematics, 29 (4), 901-924, 2003.
  425. Viatcheslav Kharlamov, Frank Sottile : Maximally inflected real rational curves
    Moscow Mathematics Journal, 3 (3), 947-987, 2003.
  426. Shrawan Kumar, Jesper Funch Thomsen: A conjectural generalization of the n! result to arbitrary groups
    Transformation Groups, 8 (1), 69-94, 2003.
  427. Antonio Laface, Luca Ugaglia : Quasi-homogeneous linear systems on P^2 with base points of multiplicity 5
    Canadian Journal of Mathematics, 55 (3), 561-575, 2003.
  428. Anton Leykin: Algorithms in computational algebraic analysis
    PhD Thesis (Minnesota University), 2003.
  429. Christoph Lossen : Singular: A Computer Algebra System
    Computing in Science and Engineering, 5 (4), 45-55, 2003.
  430. Bernd Martin : Modular Deformations and Space Curve Singularities
    Revista Matematica Iberoamericana, 19 (2), 613-621, 2003.
  431. Gábor Megyesi, Frank Sottile, Thorsten Theobald: Common transversals and tangents to two lines and two quadrics in P^3
    Discrete and Computational Geometry (Springer), 30 (4), 543-571, 2003.
  432. Gerhard Pfister : A Problem in Group Theory Solved by Computer Algebra
    Proc. of the CCASCA, Sinaia 2002, Kluwer Academic Publishers, 217-223, 2003.
  433. F. Leon Pritchard: On implicit systems of differential equations
    Journal of Differential Equations, 194 (2), 328-363, 2003.
  434. Mathias Schulze : Monodromy of Hypersurface Singularities
    Acta Applicandae Mathematicae, 75 (1-3), 3-13, 2003.
  435. Christian Sevenheck : Lagrange-Singularitäten
    Dissertation (Johannes-Gutenberg-Universität Mainz), 2003.
  436. Frank Sottile: Toric ideals, real toric varieties, and the moment map
    Proc. of AGGM, Vilnius, Lithuania. Contemporary Mathemathics, 334, 225-240, 2003.
  437. Jan Stevens : Sextic surfaces with ten triple points
    2003.
  438. Irena Swanson: The minimal components of the Mayr-Meyer ideals
    Journal of Algebra , 267 (1), 137-155, 2003.
  439. Susumu Tanabé: Combinatorial aspects of the mixed Hodge structure
    RIMS Kokyuroku "New aspects of the singularity theory", 2003.
  440. T. Theobald : New algebraic methods in computational geometry
    Habilitationsschrift, 2003.
  441. Martijn van Manen: The geometry of conflict sets
    PhD Thesis (Utrecht University, Netherlands), 2003.
  442. Ralf-Philipp Weinmann : Evaluating algebraic attacks on the AES
    Diploma Thesis (Technische Universität Darmstadt), 2003.
  443. Teijo Arponen : The complete form of a differential algebraic equation
    2002.
  444. Thomas Bayer: Moduli Spaces of Low Dimension for Semi Brieskorn-Pham Singularities w.r.t. Right Equivalence
    Proc. of the 5th CASC, 7-16, 2002.
  445. Arnaud Bodin : Non-reality and non-connectivity of complex polynomials
    Comptes Rendus Mathematique, 335 (12), 1039-1042, 2002.
  446. Antonio Campillo, José Ignacio Farrán: Symbolic Hamburger-Noether expressions of plane curves and applications to AG codes
    Mathematics of Computation, 71 (240), 1759-1780, 2002.
  447. Patrick Dondl : Modeling and Analysis of Non-Diffusive Structural Phase Transitions in Crystals
    Diploma Thesis (Bath University, UK), 2002.
  448. Jean Charles Faugère: A new efficient algorithm for computing Groebner bases without reduction to zero (F5)
    Proc. of the ISSAC'02, 75-83, 2002.
  449. Eberhard Freitag : A graded algebra related to cubic surfaces
    Kyushu Journal of Mathematics, 56 (2), 299-312, 2002.
  450. Vladimir P. Gerdt, Yuri A. Blinkov : Janet Bases of Toric Ideals
    JINR E5,11-2001-279, Dubna, Proc. of the 8th Rhine Workshop on Computer Algebra (Mannheim, Germany, 2002), 71-82, 2002.
  451. Hans-Gert Gräbe : The SymbolicData Benchmark Problems Collection of Polynomial Systems
    Proc. "Workshop on Under- and Overdetermined Systems of Algebraic or Differential Equations", Univ. Karlsruhe, 57-76, 2002.
  452. Gert-Martin Greuel, Gerhard Pfister: Computer Algebra and Finite Groups
    Proc. of the FICMS, Beijing 2002. World Scientific, 4-14, 2002.
  453. M. I. Hartillo, J. M. Ucha: A Computational Introduction to the Weyl Algebra and D-modules
    2002.
  454. Grégoire Lecerf: Quadratic Newton iteration for systems with multiplicity
    Foundations of Computational Mathematics, 2 (3), 247-293, 2002.
  455. Martijn van Manen : Applications of canonical relations in generic differential geometry
    2002.
  456. Bernd Martin : Algorithmic Computation of Flattenings and of Modular Deformations
    Journal of Symbolic Computation, 34 (3), 199-212, 2002.
  457. Michel Van den Bergh: Non-commutative crepant resolutions
    The legacy of Niels Henrik Abel, Springer, 749-770, 2002.
  458. Isabel Bermejo, Philippe Gimenez: Computing the Castelnuovo-Mumford regularity of some subschemes of P_K^n using quotients of monomial ideals
    Journal of Pure and Applied Algebra, 164 (1-2), 23-33, 2001.
  459. S. C. Coutinho, Bruno F. M. Ribeiro: On holomorphic foliations without algebraic solutions
    Experimental Mathematics, 10, 529-536, 2001.
  460. Anne Frühbis-Krüger: Computing moduli spaces for space curve singularities
    Journal of Pure and Applied Algebra, 164 (1-2), 165-178, 2001.
  461. Ryutaroh Matsumoto: Computing the radical of an ideal in positive characteristic
    Journal of Symbolic Computation, 32 (3), 263-271, 2001.
  462. Ivan W. Selesnick: Smooth wavelet tight frames with zero moments
    Applied and Computational Harmonic Analysis, 10 (2), 163-181, 2001.
  463. Doris Altmann, Klaus Altmann : Estimating Vaccine Coverage by Using Computer Algebra
    IMA Journal of Mathematics Applied in Medicine and Biology, 17, 137-146, 2000.
  464. Enrique Artal Bartolo, Ignacio Luengo Velasco, Alejandro Melle-Hernández: On the topology of a generic fibre of a polynomial function
    Communications in Algebra, 28 (4), 1767-1787, 2000.
  465. Gert-Martin Greuel: Computer Algebra and Algebraic Geometry - Achievements and Perspectives
    Journal of Symbolic Computation, 30 (3), 253-290, 2000.
  466. Anna Guerrieri, Irena Swanson: Jacobian ideals of trilinear forms: an application of 1-genericity
    Journal of Algebra, 226 (1), 410-435, 2000.
  467. Claus Hertling: Frobenius Manifolds and Variance of the Spectral Numbers
    New Developments in Singularity Theory, Proc. of the NATO Advanced Study Institute, Cambridge, 235-255, 2000.
  468. Agnes Eileen Heydtmann, Jørn Møller Jensen: On the equivalence of the Berlekamp-Massey and the Euclidean algorithms for decoding
    IEEE Transactions on Information Theory, 46 (7), 2614-2624, 2000.
  469. N. P. Kirk: Computational aspects of classifying singularities
    LMS Journal of Computation and Mathematics, 3, 207-228, 2000.
  470. I.W. Selesnick : Balanced multiwavelet bases based on symmetric FIR filters
    IEEE Trans. Signal Proc., 48, 184-191, 2000.
  471. Frank Sottile : Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro
    Experimental Mathematics, 9 (2), 161-182, 2000.
  472. Frank Sottile : Some real and unreal enumerative geometry for flag manifolds
    Michigan Math Journal, 48, 573-592, 2000.
  473. Isabel Bermejo, Philippe Gimenez: On Castelnuovo-Mumford regularity of projective curves
    Proc. of the AMS, 128 (5), 1293-1299, 1999.
  474. Anne Frühbis-Krüger: Classification of Simple Space Curve Singularities
    Communications in Algebra, 27 (8), 3993-4013, 1999.
  475. Alejandro Melle-Hernández: Euler characteristic of the Milnor fibre of plane singularities
    Proc. of the AMS, 127 (9), 2653-2655, 1999.
  476. Stephen F. Siegel, Sarah J. Witherspoon: The Hochschild cohomology ring of a group algebra
    Proc. of the LMS, 79 (1), 131-157, 1999.
  477. Massimo Caboara: Optimization of basic algorithms in Commutative Algebra
    PhD Thesis (Pisa University), 1998.
  478. Birkett Huber, Frank Sottile, Bernd Sturmfels : Numerical Schubert calculus
    Journal of Symbolic Computation, 26 (6), 767-788, 1998, Journal of Symbolic Computation 20 (1998) 767-788.
  479. Hyungju Park : Algorithms for Determining Birationality of Parametrization of Affine Curves
    1998.
  480. Mesut Şahin: Complete intersection monomial curves and non-decreasing Hilbert functions
    PhD Thesis (Bilkent University, Ankara), 2008.
  481. Xingwu Chen: Linearizability conditions of a time-reversible quartic-like system.
  482. J. Gin\'e, V.G. Romanovski: Linearizability conditions for Lotka--Volterra planar complex cubic systems
    J. Phys. A: Math. Theor., 42, 225206-225221.
  483. Jaume Gine: Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities.
  484. Eduardo Sáenz-de-Cabezón: Computing the support of monomial iterated mapping cones
    Journal of Symbolic Computation, 45 (10), 953-964.

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