Publications citing Singular

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See also Singular's entry in the swMATH database.

Introductory Textbooks

Wolfram Decker, Gerhard Pfister: A First Course in Computational Algebraic Geometry
Cambridge University Press, 2013.
Wolfram Decker, Christoph Lossen: Computing in Algebraic Geometry - A Quick Start using Singular
Springer Verlag, 2005, ACM 16.
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

Janko Boehm, Anne Frühbis-Krüger, Mirko Rahn: Massively parallel computations in algebraic geometry - not a contradiction
Computeralgebrarundbrief, 64, 8-13, 2019.
Janko Boehm: Computeralgebra - vom Vorlesungsthema zum Forschungsthema
Beiträge zum Mathematikunterricht 2018, 325-328, 2018.
Janko Boehm, Wolfram Decker, Simon Keicher, Yue Ren: Current Challenges in Developing Open Source Computer Algebra Systems
Lecture Notes in Computer Science, 9582, 3-24, 2016.
Gert-Martin Greuel, Gerhard Pfister: Singular and Applications
Jahresbericht der DMV, 108, 167-196, 2006.
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.
Christoph Lossen: Singular: A Computer Algebra System
CISE, 5 (4), 45-55, 2003.
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.
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.
Gert-Martin Greuel: Computer Algebra and Algebraic Geometry - Achievements and Perspectives
Journal of Symbolic Computation, 30 (3), 253-290, 2000.
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.
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

Singular Manual: for latest version (PDF, HTML).
Reference Card: Pdf.

Singular Presentations

Anne Frühbis-Krüger, Andreas Steenpass, Stefan Steidel: Singular 3-1-3 - Tackling New Challenges
MEGA Conference, Stockholm, Sweden, 2011.
Stefan Steidel: Singular Tutorial
Summer School in Trieste, 2008.
Gerhard Pfister: Presentation of new Implemented Algorithms
MEGA Conference, Kaiserslautern, Germany, 2003.
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.
Hans Schönemann: The system Singular
ISSAC, Lille, France, 2002.
Anne Frühbis-Krüger: A Computer Algebra System for Polynomial Computations
Mathematical Institute of Paris 6/7, 2001.
Gert-Martin Greuel: New Developments in Singularity Theory
Summer School New Developments in Singularity Theory in Cambridge, UK, 2000.
Gert-Martin Greuel, Gerhard Pfister: System und Anwendungen
DFG Tagung Effiziente Algorithmen, Karlsruhe, Germany, 2000.
Christoph Lossen: Singular presentation
Aspectos Computacionales en Álgebra Conmutativa y Geometría Algebraica, Valladolid, Spain, 2000.
Gert-Martin Greuel, Gerhard Pfister, Hans Schönemann: Singular presentation
DMV Tagung, Mainz, Germany, 1999.
Olaf Bachmann, Hans Schönemann: Monomial Representations for Groebner Bases Computations
ISSAC, Rostock, Germany, 1998.
Gert-Martin Greuel, Gerhard Pfister, Hans Schönemann: A Computer Algebra System for Polynomial Computations
ICM, Berlin, Germany, 1998.
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

Janko Boehm, Magdaleen S. Marais, Gerhard Pfister: Moduli Parameters of Complex Singularities with Non-Degenerate Newton Boundary
2024.
Dirk Basson, Janko Boehm, Magdaleen S. Marais, Mirko Rahn, Hobihasina P. Rakotoarisoa: Massively Parallel Modular Methods in Commutative Algebra and Algebraic Geometry
2024.
Janko Boehm, Wolfram Decker, Frank-Olaf Schreyer: Commutative Algebra and Algebraic Geometry using OSCAR
The Computer Algebra System OSCAR: Algorithms and Examples, Springer Cham, 21-79, 2025.
Firoozeh Aga, Janko Boehm, Alain Hoffmann, Hannah Markwig, Ali Traore: Algorithms for Gromov-Witten Invariants of Elliptic Curves
The Computer Algebra System OSCAR: Algorithms and Examples, Springer Cham, 167-190, 2025.
Zihao Wu, Janko Boehm, Rourou Ma, Hefeng Xu, Yang Zhang: NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals
Computer Physics Communications, 295, 108999, 2024.
Janko Boehm, Jesper Lykke Jacobsen, Yunfeng Jiang, Yang Zhang: Geometric Algebra and Algebraic Geometry of Loop and Potts Models
Journal of High Energy Physics, 2022, 68, 2022, 66 pp.
Dominik Bendle, Janko Boehm, Murray Heymann, Rourou Ma, Mirko Rahn, Lukas Ristau, Marcel Wittmann, Zihao Wu, Yang Zhang: pfd-parallel, a Singular/GPI-Space package for massively parallel multivariate partial fractioning
Computer Physics Communications, 294, 108942, 2024.
Janko Boehm, Magdaleen S. Marais, Gerhard Pfister: Classification of Complex Singularities with Non-Degenerate Newton Boundary
2020.
Dominik Bendle, Janko Boehm, Wolfram Decker, Alessandro Georgoudis, Franz-Josef Pfreundt, Mirko Rahn, Yang Zhang: Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals
Proceedings of Science, MA2019, 004, 2022, 19 pp.
Janko Boehm, Marcel Wittmann, Zihao Wu, Yingxuan Xu, Yang Zhang: IBP reduction coefficients made simple
Journal of High Energy Physics, 2020, 54, 2020, 39 pp.
Dominik Bendle, Janko Boehm, Yue Ren, Benjamin Schröter: Massively parallel computation of tropical varieties, their positive part, and tropical Grassmannians
Journal of Symbolic Computation, 120, 102224, 2024.
Janko Boehm, Michael Joswig, Lars Kastner, Andrew Newman: Random growth on a Ramanujan graph
2019.
Dominik Bendle, Janko Boehm, Wolfram Decker, Alessandro Georgoudis, Franz-Josef Pfreundt, Mirko Rahn, Pascal Wasser, Yang Zhang: Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
Journal of High Energy Physics, 2020, 79, 2020, 34 pp.
Janko Boehm, Christoph Goldner, Hannah Markwig: Counts of (tropical) curves in $E\times \mathbb{P}^1$ and Feynman integrals
Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions, 9, 121-158, 2022.
Janko Boehm, Christoph Goldner, Hannah Markwig: Tropical Mirror Symmetry in Dimension One
SIGMA, 18, 046, 30 pages, 2022.
Janko Boehm, Wolfram Decker, Anne Frühbis-Krüger, Franz-Josef Pfreundt, Mirko Rahn, Lukas Ristau: Towards Massively Parallel Computations in Algebraic Geometry
Foundations of Computational Mathematics, 21(3), 767-806, 2021.
Janko Boehm, Alessandro Georgoudis, Kasper J. Larsen, Hans Schoenemann, Yang Zhang: Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
Journal of High Energy Physics, 2018, 24, 2018.
Janko Boehm, Alessandro Georgoudis, Kasper J. Larsen, Mathias Schulze, Yang Zhang: Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
Physical Review D, 98, 025023, 2018.
Janko Boehm, Wolfram Decker, Claus Fieker, Santiago Laplagne, Gerhard Pfister: Bad Primes in Computational Algebraic Geometry
Lecture Notes in Computer Science, 9725, 93-102, 2016.
Janko Boehm, Magdaleen S. Marais, Gerhard Pfister: A Classification Algorithm for Complex Singularities of Corank and Modality up to Two
Singularities and Computer Algebra, Springer, 21-46, 2017.
Janko Boehm, Simon Keicher, Yue Ren: Computing GIT-fans with symmetry and the Mori chamber decomposition of $\bar{M}_{0,6}$
Mathematics of Computation, 89, 3003-3021, 2020.
Janko Boehm, Anne Frühbis-Krüger: A smoothness test for higher codimensions
Journal of Symbolic Computation, 86, 153-165, 2018.
Janko Boehm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister: Computing integral bases via localization and Hensel lifting
Journal of Symbolic Computation, 109, 283-324, 2022.
Janko Boehm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister: Local to global algorithms for the Gorenstein adjoint ideal of a curve
Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Springer, 51-96, 2017.
Andre F. van der Merwe, Janko Boehm, Magdaleen S. Marais: 3D printing dimensional calibration shape: Clebsch Cubic
Lecture Notes in Computer Science, 9725, 117-126, 2016.
Janko Boehm, Wolfram Decker, Mathias Schulze: Local analysis of Grauert-Remmert-type normalization algorithms
International Journal of Algebra and Computation, 24(1), 69-94, 2014.
Janko Boehm, Thomas Breuer: Algorithms for GIT-Fans of Affine Torus Actions
The Computer Algebra System OSCAR: Algorithms and Examples, Springer Cham, 213-224, 2025.
Burcin Erocal, Oleksandr Motsak, Frank-Olaf Schreyer, Andreas Steenpass: Refined Algorithms to Compute Syzygies
J. Symb. Comput., 74, 308-327, 2016.
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.
Janko Boehm, Magdaleen S. Marais, Andreas Steenpass: The Classification of Real Singularities Using Singular. Part III: Unimodal Singularities of Corank 2
Journal of Symbolic Computation, 99, 250-282, 2020.
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.
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.
Janko Boehm, Kathrin Bringmann, Arne Buchholz, Hannah Markwig: Tropical mirror symmetry for elliptic curves
Journal für die reine und angewandte Mathematik (Crelle's Journal), 2017, issue 732, 211-246, 2017.
Janko Boehm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister, Andreas Steenpass, Stefan Steidel: Parallel algorithms for normalization
Journal of Symbolic Computation, 51, 99-114, 2013.
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.
Janko Boehm, Wolfram Decker, Claus Fieker, Gerhard Pfister: The use of Bad Primes in Rational Reconstruction
Mathematics of Computation, 84, 3013-3027, 2015.
Christian Eder: Improving incremental signature-based Groebner basis algorithms
submitted to ISSAC 2012, 2012.
Calin-Serban Barbat: Dualization of projective algebraic sets by using Gröbner bases elimination techniques
arXiv:1101.2615, 2011.
Nazeran Idrees, Gerhard Pfister, Stefan Steidel: Parallelization of Modular Algorithms
Journal of Symbolic Computation, 46, 672-684, 2011.
Michael Monagan, Roman Pearce: Sparse polynomial division using a heap
Journal of Symbolic Computation, 46 (7), 807-822, 2011.
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.
Gert-Martin Greuel, Santiago Laplagne, Frank Seelisch: Normalization of rings
Journal of Symbolic Computation, 45 (9), 887-952, 2010.
Martin Monerjan: An Algorithm to Compute the Gröbner Fan of a Polynomial Ideal and its Implementation into SINGULAR
Universität Kaiserslautern, 2010, Diplomarbeit.
Michael Brickenstein, Alexander Dreyer : PolyBoRi: A framework for Groebner-basis computations with Boolean polynomials
Journal of Symbolic Computation, 44 (9), 1326-1345, 2009.
Anders Nedergaard Jensen, Hannah Markwig, Thomas Markwig: An algorithm for lifting points in a tropical variety
Collectanea Mathematica, 59 (2), 129-165, 2008.
Anne Frühbis-Krüger, Gerhard Pfister: Algorithmic Resolution of Singularities
Lecture Notes of LMS, Cambridge University Press, 2006.
Michael Brickenstein : Slimgb: Gröbner bases with slim polynomials
Reports on Computer Algebra (ZCA, University of Kaiserslautern), 35, 2005.
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.
Viktor Levandovskyy : Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation
PhD Thesis (University of Kaiserslautern), 2005.
Mathias Schulze : Good bases for tame polynomials
Journal of Symbolic Computation, 39 (1), 103-126, 2005.
E. A. Tobis : Libraries for Counting Real Roots
Reports on Computer Algebra (ZCA, University of Kaiserslautern), 34, 2005.
Anne Frühbis-Krüger, Gerhard Pfister: Practical Aspects of Algorithmic Resolution of Singularities
Reports on Computer Algebra (ZCA, University of Kaiserslautern), 33, 2004.
Mathias Schulze : A normal form algorithm for the Brieskorn lattice
Journal of Symbolic Computation, 38 (4), 1207-1225, 2004.
Anne Frühbis-Krüger, Kai Krüger, Hans Schönemann: Dynamic Modules in Singular
Reports on Computer Algebra (ZCA, University of Kaiserslautern), 32, 2003.
Viktor Levandovskyy : PBW Bases, Non-Degeneracy Conditions and Applications
Proc. of the ICRA X conference, Toronto, Canada. Fields Institute, 2003.
Viktor Levandovskyy, Hans Schönemann: PLURAL - a Computer Algebra System for Noncommutative Polynomial Algebras
Proc. of the ISSAC 2003, Philadelphia, USA, 2003.
I Made Sulandra: Über Gröbnerwalkalgorithmen
PhD Thesis (Universität des Saarlandes), 2003.
F. Hernando : Computation of the Alexander polynomial of a plane curve singularity and an implementation in Singular
Master Thesis (University of Kaiserslautern), 2002.
Viktor Levandovskyy : On Gröbner bases for noncommutative G-algebras
Proc. of the 8th Rhine Workshop on Computer Algebra, Mannheim, Germany, 2002.
Chris Monico: Computing the primary decomposition of zero-dimensional ideals
Journal of Symbolic Computation, 34 (5), 451-459, 2002.
Hans Schönemann: Data representations in the computer algebra system Singular
Workshop on Applications of Commutative Algebra, Catania, 2002.
Mathias Schulze : The differential structure of the Brieskorn lattice
A. M. Cohen et al.: Mathematical Software - ICMS 2002, World Scientific, 136-146, 2002.
Mathias Schulze : Algorithmic Gauss-Manin Connection
PhD Thesis (University of Kaiserslautern), 2002.
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.
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.
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.
Mathias Schulze : Algorithms for the Gauss-Manin connection
Journal of Symbolic Computation, 32 (5), 549-564, 2001.
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.
Thomas Bayer : Computation of moduli spaces for semiquasihomogenous singularities and an implementation in Singular
Diploma Thesis (University of Kaiserslautern), 2000.
T. Siebert : Recursive Computation of Free Resolutions and a Generalized Koszul Complex
Reports on Computer Algebra (ZCA, University of Kaiserslautern), 28, 2000.
Agnes Eileen Heydtmann: Generating Invariant Rings of Finite Groups
Diploma Thesis (Universität des Saarlandes), 1999.
Dietmar Hillebrand : Triangulierung nulldimensionaler Ideale - Implementierung und Vergleich zweier Algorithmen
Diploma Thesis (Universität Dortmund), 1999.
Martin Lamm : Hamburger-Noether Entwicklung von Kurvensingularitäten
Diploma Thesis (University of Kaiserslautern), 1999.
Hans Schönemann : Polynomials in Factory and Singular
Nikolaus-Konferenz Aachen, 1999.
Mathias Schulze : Computation of the Monodromy of an Isolated Hypersurface Singularity
Diploma Thesis (University of Kaiserslautern), 1999.
Christine Theis : Der Buchberger-Algorithmus für torische Ideale und seine Anwendung in der ganzzahligen Optimierung
Diploma Thesis (Universität des Saarlandes), 1999.
Moritz Wenk : Resultantenmethoden zur Lösung algebraischer Gleichungssysteme implementiert in Singular
Diploma Thesis (University of Kaiserslautern), 1999.
O. Bachmann, Hans Schönemann : Monomial Representations for Groebner Basis Computations
Reports on Computer Algebra (ZCA, University of Kaiserslautern), 18, 1998.
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.
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.
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.
Wolfram Decker, Theo de Jong : Gröbner bases and invariant theory
Gröbner bases and applications, London Math. Soc. Lecture Notes Series, 251, 61-89, 1998.
Bernd Martin : Computing versal deformations with singular
G.-M. Greuel, B. H. Matzat, G. Hiss: Algorithmic Algebra and Number Theory (Springer), 283-294, 1998.
O. Bachmann, S. Gray, Hans Schönemann : MP Prototype Specification
Reports on Computer Algebra (ZCA, University of Kaiserslautern), 12, 1997.
Kai Krüger: Klassifikation von Hyperflächensingularitäten
Diploma Thesis (University of Kaiserslautern), 1997.
Tim Wichmann : Der FGLM Algorithmus - verallgemeinert und implementiert in Singular
Diploma Thesis (University of Kaiserslautern), 1997.
Olaf Bachmann, Simon Gray, Hans Schönemann: MPP: a framework for distributed polynomial computations
Proc. of the ISSAC, Zurich, Switzerland, 103-112, 1996.
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.
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.
Hans Schönemann : Algorithms in Singular
Reports on Computer Algebra (ZCA, University of Kaiserslautern), 2, 1996.
T. Siebert : On strategies and implementations for computations of free resolutions
Reports on Computer Algebra (ZCA, University of Kaiserslautern), 8, 1996.
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

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.
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.
Timo Erkama, Samuli Piipponen: Rational Cycles of Quadratic Polynomials
JP Journal of Algebra, Number Theory and Applications, 33, 113-132, 2014.
Teijo Arponen, Samuli Piipponen, Jukka Tuomela: Classification of Singularities in Kinematics of Mechanisms
Mechanisms and Machine Science, 15, 41-48, 2013.
Samuli Piipponen, Jukka Tuomela: Algebraic analysis of kinematics of multibody systems
Mechanical Sciences, 4, 33-47, 2013.
Samuli Piipponen, Jukka Tuomela: Configuration space analysis of rigid mechanisms
Miskolc Mathematical Notes , 14, 685-695, 2013.
Viktor Levandovskyy, Jorge Martín-Morales: Algorithms for checking rational roots of b-functions and their applications
Journal of Algebra, 352, 408-429, 2012.
Iwona Krzyżanowska: The intersection number of real polynomial mappings
Topology and its Applications, 158, 379-386, 2011, issue 3.
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.
Anne Frühbis-Krüger: Some Remarks on Blowing-Ups in a Computer Algebra System
Computer Science Journal of Moldova, 16, 15--34, 2008.
Valery Romanovski, Douglas Shafer: The Center and Cyclicity Problems. A Computational Algebra Approach
Birkhäuser, 2008.
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.
Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin: Introduction to Singularities and Deformations
Springer Monographs in Mathematics, 2007.
Bernd Sturmfels: Solving Systems of Polynomial Equations
CBMS Regional Conference Series in Mathematics, AMS, Providence, 97, 2002.
David A. Cox, John B. Little, Donal O'Shea: Using Algebraic Geometry
Springer Verlag, 1998.
David A. Cox, John B. Little, Donal O'Shea: Ideals, Varieties, and Algorithms
Springer Verlag, 1997.

Further Publications Referring to Singular

Wolfram Decker, Christian Eder, Claus Fieker, Max Horn, Michael Joswig (eds.): The Computer Algebra System OSCAR: Algorithms and Examples
Algorithms and Computation in Mathematics, Springer Cham, 2025.
Thorsten Theobald: An enumerative geometry framework for algorithmic line problems in R^3
SIAM Journal on Computing, 31 (4), 1212-1228, SIAM.
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.
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.
Teijo Arponen, Samuli Piipponen, Jukka Tuomela: Kinematical analysis of Wunderlich mechanism
Mechanism and Machine Theory, 70, 16-31, 2013.
Hiep Dang: Computations in multivariate quaternionic polynomial ring
Le Matematiche, LXVIII, 3-11, 2013.
Marcin Dumnicki, Tomasz Szemberg, Halszka Tutaj-Gasinska: A counter-example to a question by Huneke and Harbourne
2013, arXiv:1301.7440.
Akihito Kikuchi: An approach to first principles electronic structure calculation by symbolic-numeric computation
Qscience connect , Bloomsbury Qatar Foundation Journals, 2013, No.1, 2013.
Federico Ardila, Megan Owen, Seth Sullivant: Geodesics in CAT(0) cubical complexes
Advances in Applied Mathematics, 48 (1), 142-163, 2012.
G. Dibitetto, A. Guarino, D. Roest: Vacua analysis in extended supersymmetry compactifications
Progress of Physics, 60 (3), 2012.
Amir Hashemi: Efficient computation of Castelnuovo-Mumford regularity
Mathematics of Computation, 81, 1163-1177, 2012.
Nathan Owen Ilten, Lars Kastner: Calculating Generators of Multigraded Algebras
2012.
Akihito Kikuchi: A proposal to first principles electronic structure calculation:Symbolic-Numeric method
preprint, 2012, 42.
David J. Marchette: Minimal Free Resolutions of Graph Edge Ideals
2012.
Bernd Martin, Dmitry Pochekutov: Discriminant and Singularities of Logarithmic Gauss Map, Examples and Application
2012.
Jeaman Ahn, Sijong Kwak, YeongSeok Song: Generic Initial ideals of Singular Curves in Graded Lexicographic Order
2011.
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.
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.
Gwénolé Ars, Amir Hashemi: Computing Syzygies by Faugère's F_5 Algorithm
Results in Mathematics, 59 (1-2), 35-42, 2011.
Daniel J. Bates, Luke Oeding: Toward a salmon conjecture
Experimental Mathematics, 20 (3), 358–370, 2011.
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.
Janko Boehm, David Eisenbud, Max Nitsche: Decomposition of semigroup algebras
to appear in Experimental Mathematics, 2011.
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.
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.
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.
Christian Eder, John Perry: Signature-based algorithms to compute Groebner bases
submitted to ISSAC 2011, 16 pages, 2011.
Graham Ellis, Paul Smith: Computing group cohomology rings from the Lyndon-Hochschild-Serre spectral sequence
Journal of Symbolic Computation, 46 (4), 360-370, 2011.
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.
Raul M. Falcón: The set of autotopisms of partial Latin squares
arXiv:1107.3248v1 [math.CO], 2011.
David J. Green, Simon King: The computation of the cohomology rings of all groups of order 128
Journal of Algebra, 325, 352-363, 2011.
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.
Dang Tuan Hiep: Computing Serre\'s Intersection Multiplicities
2011.
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.
Shutaro Inoue, Katsusuke Nabeshima, Ko Sakai, Yosuke Sato, Akira Suzuki: Boolean Gröbner bases
Journal of Symbolic Computation, 46 (5), 622-632, 2011.
Sebastian Jambor: Computing minimal associated primes in polynomial rings over the integers
Journal of Symbolic Computation, 46 (10), 1098-1104, 2011.
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.
Iwona Krzyżanowska, Zbigniew Szafraniec: Polynomial mappings into a Stiefel manifold and immersions
2011.
Margreta Kuijper, Kristina Schindelar: Minimal Gröbner bases and the predictable leading monomial property
Linear Algebra and its Applications, 434 (1), 104-116, 2011.
Zbigniew Leśniak Leśniak, Yong-Guo Shi: One class of planar rational involutions
Nonlinear Analysis: Theory, Methods & Applications, 74 (17), 6097-6104, 2011.
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.
Ulrich Loup, Erika Ábrahám: GiNaCRA: A C++ Library for Real Algebraic Computations
Lecture Notes in Computer Science, 6617, 512-517, 2011.
Agustin Marcelo, Peter Schenzel: Non-Cohen-Macaulay unique factorization domains in small dimensions
Journal of Symbolic Computation, 46 (5), 609-621, 2011.
Dhagash Mehta: Numerical Polynomial Homotopy Continuation Method and String Vacua
Advances in High Energy Physics, 2011, 15, 2011.
Dorin Popescu: Depth of factors of square free monomial ideals
2011.
Johannes Rauh: Finding the Maximizers of the Information Divergence from an Exponential Family
IEEE Transactions on Information Theory, 57 (6), 3236-3247, 2011.
Elizabeth A. Sell: On splice quotients of the form {z^n = f(x,y)}
Mathematische Nachrichten, 284 (10), 1286-1303, 2011.
Yi-Huang Shen: Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three
Communications in Algebra, 39 (5), 1922-1940, 2011.
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.
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.
Jinpeng An, Dragomir Ž. Đoković: Zero patterns and unitary similarity
Journal of Algebra, 324 (1), 51-80, 2010.
Jingeng An, Dragomir Z. Dokovic: Zero Patterns and Unitary Similarity
Journal of Algebra, 324 (1), 51-80, 2010.
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.
Daniel Andres, Viktor Levandovskyy, Jorge Martin-Morales: Effective Methods for the Computation of Bernstein-Sato polynomial for Hypersurfaces and Affine Varieties
2010.
Rémi Arcadias: Multidegree for bifiltered D-modules
2010.
Mohamed Barakat, Markus Lange-Hegermann : An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization
JPAA, 2010.
Tanja Becker: On the existence of symplectic resolutions of symplectic reductions
Mathematische Zeitschrift, 265 (2), 343-363, 2010.
Christine Berkesch, Anton Leykin: Algorithms for Bernstein-Sato polynomials and multiplier ideals
2010.
Cinzia Bisi, Francesco Polizzi: On Proper Polynomial Maps of C^2
Journal of Geometric Analysis, 20, 72-89, 2010.
Yousra Boubakri, Gert-Martin Greuel, Thomas Markwig: Invariants of Hypersurface Singularities in Positive Characteristic
2010.
Volker Braun : Three generations on the quintic quotient
Journal of High Energy Physics, 2010 (1), 1-18, 2010.
Michael Brickenstein, Stanislav Bulygin : Obtaining and solving systems of equations in key variables only for the small variants of AES
Mathematics in Computer Science, 3 (2), 185-200, 2010.
Andries E. Brouwer, Mihaela Popoviciu : The invariants of the binary nonic
Journal of Symbolic Computation, 45 (6), 709-720, 2010.
Johannes Buchmann, Stanislav Bulygin, Albrecht Petzoldt: Selecting Parameters for the Rainbow Signature Scheme
PQCrypto 2010, Lecture Notes in Computer Science / Springer, 6061, 218-240, 2010.
Stanislav Bulygin, Ruud Pellikaan : Decoding and finding the minimum distance with Gröbner bases: history and new insights
World Scientific, 585-622, 2010.
Xingwu Chen, Valery G. Romanovski: Linearizability conditions of time-reversible cubic systems
Journal of Mathematical Analysis and Applications, 362 (2), 438-449, 2010.
Aldo Conca, Tim Römer: Generic initial ideals and fibre products
Osaka Journal of Mathematics, 47 (1), 17-32, 2010.
Guillermo Cortiñas, Christian Haesemeyer, Mark E. Walker, Charles Weibel: A negative answer to a question of Bass
2010.
Alberto Damiano, Graziano Gentili, Daniele Struppa: Computations in the ring of quaternionic polynomials
Journal of Symbolic Computation, 45 (1), 38-45, 2010.
Ruchira S. Datta : Finding all Nash equilibria of a finite game using polynomial algebra
Economic Theory, Springer, 42 (1), 55-96, 2010.
Alicia Dickenstein, Laura Felicia Matusevich, Ezra Miller: Combinatorics of binomial primary decomposition
Mathematische Zeitschrift, 264 (4), 745-763, 2010.
Christian Eder, Justin Gash, John Perry: Modifying Faugère's F5 Algorithm to ensure termination
19 pages, 2010, accepted for publication on the ACM SIGSAM Communications in Computer Algebra.
Christian Eder, John Perry: F5C: a variant of Faugere's F5 algorithm with reduced Groebner bases
Journal of Symbolic Computations (MEGA2009 special issue), 45(12), 1442-1458, 2010.
Viviana Ene, Anda Olteanu, Loredana Sorrenti: Properties of lexsegment ideals
Osaka Journal of Mathematics, 47 (1), 67-87, 2010.
Viviana Ferrer, Israel Vainsencher : Polynomial vector fields with algebraic trajectories
2010.
Anne Frühbis-Krüger, Alexander Neumer: Simple Cohen-Macaulay Codimension 2 Singularities
Communications in Algebra, 38 (2), 454-495, 2010.
Anne Frühbis-Krüger: A Short Note on Hauser's Kangaroo Phenomena and Weak Maximal Contact in Higher Dimensions
Journal of Singularities, 2, 128--142, 2010.
Carlos Galindo, Francisco Monserrat: On the Characterization of Algebraically Integrable Plane Foliations
Transactions of the AMS, 362 (9), 4557-4568, 2010.
Jaume Giné, Valery G. Romanovski: Integrability conditions for Lotka–Volterra planar complex quintic systems
Nonlinear Analysis: Real World Applications, 11 (3), 2100-2105, 2010.
Gert-Martin Greuel, Frank Seelisch, Oliver Wienand: The Groebner basis of the ideal of vanishing polynomials
JSC special issue on 'Groebner Bases and their Applications', 2010.
Eleonora Guerrini, Emmanuela Orsini, Massimiliano Sala: Computing the distance distribution of systematic nonlinear codes
Journal of Algebra and its Applications, 9 (2), 241-256, 2010.
Amina Hadj Kacem, Ihsen Yengui: Dynamical Gröbner bases over Dedekind rings
Journal of Algebra, 324 (1) , 12-24, 2010.
Maoan Han, Valery G. Romanovski: Estimating the number of limit cycles in polynomials systems
Journal of Mathematical Analysis and Applications, 368 (2), 491-497, 2010.
Franziska Hinkelmann, Reinhard Laubenbacher, David Murrugarra, Abdul Salam Jarrah: A Mathematical Framework for Agent Based Models of Complex Biological Networks
2010.
Hans Jockers, Peter Mayr, Johannes Walcher: On N=1 4d Effective Couplings for F-theory and Heterotic Vacua
Advances in Theoretical and Mathematical Physics, 14 (5), 1433-1514, 2010.
Michal Kapustka: Geometric transitions between Calabi-Yau threefolds related to Kustin-Miller unprojections
2010.
Iwona Karolkiewicz, Aleksandra Nowel, Zbigniew Szafraniec: An algebraic formula for the intersection number of a polynomial immersion
Journal of Pure and Applied Algebra, 214 (3), 269-280, 2010.
Hideyasu Kawai: Construction of Maximal Ideals of Commutative Group Algebras
International Journal of Algebra and Computation, 20 (3), 381-389, 2010.
Dmitry Kerner: On some generalizations of Newton non-degeneracy for hypersurface singularities
Journal of the LMS, 82 (1), 49-73, 2010.
Johanna Knapp, Emanuel Scheidegger: Matrix factorizations, Massey products and F-terms for two-parameter Calabi-Yau hypersurfaces
Advances in Theoretical and Mathematical Physics, 14 (1), 225-307, 2010.
Ulrich Kraemer, Elmar Wagner: A residue formula for the fundamental Hochschild class of the Podles sphere
2010.
Felix E. Kubler, Karl H. Schmedders: Competitive Equilibria in Semi-Algebraic Economies
Journal of Economic Theory, 145 (1), 301-330, 2010.
Simon Kurmann: Partial elimination ideals and secant cones
2010.
Manfred Lehn, Y. Namikawa, Christoph Sorger: Slodowy Slices and Universal Poisson Deformations
2010.
Huishi Li: Lifting Gröbner Bases from a Class of Algebras
Communications in Algebra, 38 (6), 2282-2299, 2010.
Huishi Li: Looking for Gröbner basis theory for (almost) skew 2-nomial algebras
Journal of Symbolic Computation, 45 (9), 918-942, 2010.
Hossein Movasati: Eisenstein type series for Calabi-Yau varieties
2010.
Hajime Nagoya, Juanjuan Sun: Confluent KZ equations for sl_N with Poincare rank 2 at infinity
2010.
Jiawang Nie: Discriminants and Nonnegative Polynomials
2010.
Kenta Nishiyama, Masayuki Noro: Stratification associated with local b-functions
Journal of Symbolic Computation, 45 (4), 462-480, 2010.
Alfons I. Ooms, Michel Van den Bergh: A degree inequality for Lie algebras with a regular Poisson semi-center
Journal of Algebra, 323 (2), 305-322, 2010.
Asia Rauf: A procedure to compute prime filtration
Central European Journal of Mathematics, 8 (1), 26-31, 2010.
Afshan Sadiq: F4 Algorithm For Euclidean Rings
2010.
Mathias Schulze: Logarithmic comparison theorem versus Gauss-Manin system for isolated singularities
Advances in Geometry, 10 (4), 699-708, 2010.
Fernando San Segundo, Juan Rafael Sendra: Total Degree Formula for the Generic Offset to a Parametric Surface
2010.
Bernd Sturmfels, Caroline Uhler: Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry
Annals of the Institute of Statistical Mathematics, 62, 2010.
Hirotachi Abo, Giorgio Ottaviani, Chris Peterson: Induction for secant varieties of Segre varieties
Transactions of the AMS, 361 (2), 767-792, 2009.
Ibrahim Al-Ayyoub: Normality of Monomial Ideals
Rocky Mountain Journal of Mathematics, 39 (1), 1-9, 2009.
Martin Albrecht, Carlos Cid : Algebraic Techniques in Differential Cryptanalysis
Lecture Notes in Computer Science, 5665, 193-208, 2009.
Fernando Antoneli, Patricia Hernandes Baptistelli, Ana Paula S. Dias, Miriam Garcia Manoel: Invariant theory and reversible-equivariant vector fields
Journal of Pure and Applied Algebra, 213 (5), 649-663, 2009.
Teijo Arponen, Samuli Piipponen, Jukka Tuomela: Kinematic analysis of Bricard's mechanism
Nonlinear Dynamics, 56 (1-2), 85-99, 2009.
Feza Arslan, Pinar Mete, Mesut Şahin: Gluing and Hilbert functions of monomial curves
Proc. of the AMS, 137 (7), 2225-2232, 2009.
Gregory V. Bard : Algebraic Cryptanalysis
Springer Publishing Company, 2009.
B. Ross Barmish, Fabrizio Dabbene, Sheila R. Ross, Pavel S. Shcherbakov: On positivity of polynomials: the dilation integral method
IEEE Transactions on Automatic Control, 54 (5), 965-978, 2009.
Daniel J. Bates, Jonathan D. Hauenstein, Chris Peterson, Andrew J. Sommese : Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials
Texts and Monographs in Symbolic Computation, 55-77, 2009.
Dan Bates, Frank Sottile : Khovanskii-Rolle continuation for real solutions
2009.
Dave Bayer, Amelia Taylor: Reverse search for monomial ideals
Journal of Symbolic Computation, 44 (10), 1477-1486, 2009.
Georgia Benkart, Mariana Pereira, Sarah Witherspoon : Yetter-Drinfeld modules under cocycle twists
2009.
Cinzia Bisi, Francesco Polizzi: Proper polynomial self-maps of the affine space: state of the art and new results
to appear in: Contemporary Mathematics, Proceedings of Complex Analysis and Dynamical Systems IV, 2009.
Carles Bivià-Ausina, Santiago Encinas: Łojasiewicz exponents and resolution of singularities
Archiv der Mathematik, 93 (3), 225-234, 2009.
Carles Bivià-Ausina: Local Łojasiewicz exponents, Milnor numbers and mixed multiplicities of ideals
Mathematische Zeitschrift, 262 (2), 389-409, 2009.
Rocio Blanco: Complexity of Villamayor's algorithm in the non-exceptional monomial case
International Journal of Mathematics, 20 (6), 659-678, 2009.
M. Borges-Quintana, M.A. Borges-Trenard, E. Martinez-Moro : An Application of Möller's Algorithm to Coding Theory
Gröbner Bases, Coding, and Cryptography (Springer), 379-384, 2009.
Yousra Boubakri: Hypersurface singularities in positive characteristic
PhD Thesis (TU Kaiserslautern), 2009.
Michael Brickenstein : Slimgb: Gröbner bases with slim polynomials
Revista Matemática Complutense, 2009.
Michael Brickenstein, Alexander Dreyer, Gert-Martin Greuel, Markus Wedler, Oliver Wienand: New developments in the theory of Gr�bner bases and applications to formal verification
Journal of Pure and Applied Algebra, 213 (8), 1612-1635, 2009.
Markus Brodmann, Peter Schenzel: Projective Curves with maximal regularity and applications to syzygies and surfaces
2009.
Winfried Bruns, Joseph Gubeladze: Polytopes, Rings and K-Theory
Springer Monographs in Mathematics, 2009.
Stanislav Bulygin, Ruud Pellikaan : Bounded distance decoding of linear error-correcting codes with Gröbner bases
Journal of Symbolic Computation, 44 (12), 1626-1643, 2009.
Stanislav Bulygin, Ruud Pellikaan : Decoding linear error-correcting codes up to half the minimum distance with Gröbner bases
Gröbner Bases, Coding, and Cryptography (Springer), 361-365, 2009.
Nils Carqueville : Matrix factorisations and open topological string theory
Journal of High Energy Physics, 2009 (7), 5-?, 2009.
Nils Carqueville, Ingo Runkel : On the monoidal structure of matrix bi-factorisations
2009.
Dustin A. Cartwright, Daniel Erman, Mauricio Velasco, Bianca Viray: Hilbert schemes of 8 points
Algebra & Number Theory, 3 (7), 763-795, 2009.
Colin Christopher, Jaume Llibre, Chara Pantazi, Sebastian Walcher: Inverse problems for invariant algebraic curves: explicit computations
Proc. of the Royal Society of Edinburgh: Section A Mathematics, 139 (2), 287-302, 2009.
Robert M. Corless, Karin Gatermann, Ilias S. Kotsireas: Using symmetries in the eigenvalue method for polynomial systems
Journal of Symbolic Computation, 44 (11), 1536-1550, 2009.
S. C. Coutinho, Marcos da Silva Ferreira: Algebraic solutions of Jacobi equations
Mathematics of Computation, AMS, 78 (268), 2427-2433, 2009.
S. C. Coutinho, Luis Menasché Schechter: Algebraic solutions of plane vector fields
Journal of Pure and Applied Algebra, 213 (1), 144-153, 2009.
Fernando Cukierman, J. V. Pereira, Israel Vainsencher: Stability of foliations induced by rational maps
Annales de la faculté des sciences de Toulouse, 18 (4), 685-715, 2009.
Alberto Damiano, Daniele Struppa, Adrian Vajiac, Mihaela Vajiac: Hartogs Phenomena and Antisyzygies for Systems of Differential Equations
Journal of Geometric Analysis, 19 (2), 288-300, 2009.
Nivaldo de Góes Grulha, Jr.: The Euler obstruction and Bruce-Roberts' Milnor number
The Quarterly Journal of Mathematics, 60 (3), 291-302, 2009.
Marc Dohm : Implicitization of rational ruled surfaces with [mu]-bases
Journal of Symbolic Computation, 2009.
Mirela Domijan, Markus Kirkilionis: Bistability and oscillations in chemical reaction networks
Journal of Mathematical Biology, 59 (4), 467-501, 2009.
Patrick W. Dondl, Kai Hormann, Johannes Zimmer : Modeling transformation paths of multiphase materials: The triple point of zirconia
Phys. Rev. B, 79 (10), 2009.
Mathias Drton: Discrete chain graph models
Bernoulli, 15 (3), 736-753, 2009.
Mathias Drton: Likelihood ratio tests and singularities
The Annals of Statistics, 37(2), 979-1012, 2009.
Wolfgang Ebeling, S. M. Gusein-Zade : On indices of 1-forms on determinantal singularities
Proc. of the Steklov Institute of Mathematics, 267 (1), 113-124, 2009.
Christian Eder : On The Criteria Of The F5 Algorithm
preprint, 2009.
Eivind Eriksen, Trond Stølen Gustavsen: Lie-Rinehart cohomology and integrable connections on modules of rank one
Journal of Algebra, 322 (12), 4283-4294, 2009.
Philip Foth, Sangjib Kim : Toric degenerations of Bott-Samelson varieties
2009.
Carlos Galindo, Francisco Monserrat: δ-Sequences and evaluation codes defined by plane valuations at infinity
Proc. of the London Mathematical Society, 98 (3), 714-740, 2009.
Juan Ignacio Garcia Garcia, F. J. Lobillo, Jesus Garcia Miranda: Elimination orderings and localization in PBW algebras
Linear Algebra and its Applications, 430 (8-9), 2133-2148, 2009.
Eberhard H.-A. Gerbracht: Eleven Unit Distance Embeddings of the Heawood Graph
2009.
James Gray, Yang-Hui He, Anton Ilderton, André Lukas : STRINGVACUA: A Mathematica Package for Studying Vacuum Configurations in String Phenomenology
Comput. Phys. Commun., 180, 107-119, 2009.
Ignacio de Gregorio, David Mond, Christian Sevenheck: Linear free divisors and Frobenius manifolds
Compositio Mathematica, 145 85), 1305-1350, 2009.
Eleonora Guerrini, Emmanuela Orsini, Ilaria Simonetti: Gröbner Bases for the Distance Distribution of Systematic Codes
Gröbner Bases, Coding, and Cryptography (Springer), 367-372, 2009.
Johannes Härtel: Reduktionssysteme zur Berechnung einer Auflösung der orthogonalen freien Quantengruppen $A_o(n)$
2009.
Raymond Hemmecke, Peter N. Malkin: Computing generating sets of lattice ideals and Markov bases of lattices
Journal of Symbolic Computation, 44 (10), 1463-1476, 2009.
Manuel A. Insua, Manuel Ladra: Gröbner bases in universal enveloping algebras of Leibniz algebras
Journal of Symbolic Computation, 44 (5), 517-526, 2009.
Abdul S. Jarrah, Reinhard Laubenbacher : On the algebraic geometry of polynomial dynamical systems
Emerging Applications of Algebraic Geometry, IMA Vol. Math. Appl., 149, 109-123, 2009.
Grzegorz Kapustka: Primitive contractions of Calabi-Yau threefolds II
Journal of the London Math. Soc., 79 (1), 259-271, 2009.
Grzegorz Kapustka, Michal Kapustka : A cascade of determinantal Calabi-Yau threefolds
2009.
Grzegorz Kapustka, Michal Kapustka: Primitive contractions of Calabi-Yau threefolds I
Communications in Algebra, 37 (2), 482-502, 2009.
Eric Katz, Hannah Markwig, Thomas Markwig: The tropical j-invariant
LMS Journal of Computation and Mathematics , 12, 275-294, 2009.
Junaid Alam Khan: Converting Subalgebra Bases with the Sagbi Walk
2009.
Junaid Alam Khan: Subalgebra Analogue to Standard Basis for Ideal
2009.
A. Kuleshov, Alexander A. Reshetnyak: Programming Realization of Symbolic Computations for Non-linear Commutator Superalgebras over the Heisenberg--Weyl Superalgebra: Data Structures and Processing Methods
2009.
Roberto La Scala, Viktor Levandovskyy: Letterplace ideals and non-commutative Gröbner bases
Journal of Symbolic Computation, 44 (10), 1374-1393, 2009.
Oliver Labs : A Septic with 99 real Nodes
Rend. Sem. Mat. Univ. Pad., 116, 299-313, 2009.
Antonio Laface, Luca Ugaglia: On multiples of divisors associated to Veronese embeddings with defective secant variety
Bulletin of the Belgian Mathematical Society, 16 (5), 933-942, 2009.
Mathias Lederer: Finite sets of d-planes in affine space
Journal of Algebra, 321 (12), 3827-3849, 2009.
Douglas A. Leonard: A weighted module view of integral closures of affine domains of type I
Advances in Mathematics of Communications, 3 (1), 1-11, 2009.
Viktor Levandovskyy, Valery G. Romanovski, Douglas S. Shafer: The cyclicity of a cubic system with nonradical Bautin ideal
Journal of Differential Equations, 246 (3), 1274-1287, 2009.
Miguel Ángel Marco-Buzunariz, Jorge Martín-Morales : Graded Betti Numbers of the Logarithmic Derivation Module
2009.
Bernd Martin, Hendrik Süß: Milnor algebras could be isomorphic to modular algebras
Journal of Symbolic Computation, 44 (9), 1268-1279, 2009.
R. Matsumoto : Radical Computation for Small Characteristics
Gröbner Bases, Coding, and Cryptography (Springer), 427-430, 2009.
Dhagash Mehta, Andre Sternbeck, Lorenz von Smekal, Anthony G. Williams : Lattice Landau Gauge and Algebraic Geometry
PoS QCD-TNT, 9, 2009.
Jorge Neves, Stavros Argyrios Papadakis: A construction of numerical Campedelli surfaces with torsion Z/6
Transactions of the AMS, 361 (9), 4999-5021, 2009.
Jiawang Nie, Kristian Ranestad: Algebraic Degree of Polynomial Optimization
SIAM Journal on Optimization, 20 (1), 485-502, 2009.
Alfons I. Ooms: Computing invariants and semi-invariants by means of Frobenius Lie algebras
Journal of Algebra, 321 (4), 1293-1312, 2009.
Samuli Piipponen: Singularity analysis of planar linkages
Multibody System Dynamics, 22, 223-243, 2009.
Daniel Robertz: Noether normalization guided by monomial cone decompositions
Journal of Symbolic Computation, 44 (10), 1359-1373, 2009.
Sönke Rollenske : The Kuranishi-space of complex parallelisable nilmanifolds
JEMS, 2009.
Afshan Sadiq : Standard Bases over Rings
2009.
Mathias Schulze, Uli Walther: Cohen-Macaulayness and computation of Newton graded toric rings
Journal of Pure and Applied Algebra, 213 (8), 1522-1535, 2009.
Jan Stevens: Universal abelian covers of superisolated singularities
Mathematische Nachrichten, 282 (8), 1195-1215, 2009.
Bernd Sturmfels : Open Problems in Algebraic Statistics
Emerging Applications of Algebraic Geometry (IMA Vol. Math. App.), 149, 351-363, 2009.
Raimundas Vidunas, Alexander Kitaev: Computation of highly ramified coverings
Mathematics of Computation, AMS, 78 (268), 2371-2395, 2009.
Martin Albrecht, Daniel Augot, Anne Canteaut, Carlos Cid, Ralf-Phillip Weinmann: Algebraic Cryptanalysis of Symmetric Primitives
ECRYPT Report (D.STVL.7), 2008.
Max A. Alekseyev, Pavel A. Pevzner: Multi-Break Rearrangements and Chromosomal Evolution
Theoretical Computer Science, 395 (2-3), 193-202, 2008.
Elizabeth S. Allman, John A. Rhodes : Identifying evolutionary trees and substitution parameters for the general Markov model with invariable sites
Mathematical Biosciences, 211 (1), 18-33, 2008.
Klaus Altmann: Algebraische Geometrie
2008.
Teijo Arponen, Samuli Piipponen, Jukka Tuomela : Analysing singularities of a benchmark problem
Multibody System Dynamics, 19 (3), 227-253, 2008.
Patrícia Hernandes Baptistelli, Miriam Garcia Manoel: The σ-isotypic decomposition and the σ-index of reversible-equivariant systems
2008.
Mohamed Barakat, Daniel Robertz: homalg - A Meta-Package for Homological Algebra
Journal of Algebra and its Applications, 7 (3), 299-317, 2008.
Frank Bauer: Split operators for oblique boundary value problems
Applicable Analysis, 87 (1), 45-57, 2008.
Arkady Berenstein, Sebastian Zwicknagl: Braided Symmetric and Exterior Algebras
Transactions of the AMS, 360 (7), 3429-3472, 2008.
Frederic Bihan, J. Maurice Rojas, Frank Sottile : On the sharpness of fewnomial bounds and the number of components of fewnomial hypersurfaces
Algorithms in algebraic geometry, IMA Vol. Math. Appl., 146, 15-20, 2008.
Volker Braun, Tamaz Brelidze, Michael R. Douglas, Burt A. Ovrut: Calabi-Yau metrics for quotients and complete intersections
Journal of High Energy Physics, 5, 2008.
Michael Brickenstein, Alexander Dreyer: Groebner-free normal forms for boolean polynomials
ISSAC 2008, 55-62, 2008.
Lance Bryant: Goto Numbers of a Numerical Semigroup Ring and the Gorensteiness of Associated Graded Rings
2008.
Igor Burban, Yuriy Drozd: Maximal Cohen-Macaulay Modules over Surface Singularities
Trends in representation theory of algebras and related topics, EMS Publishing House, 101-166, 2008.
Nils Carqueville : Triangle-generation in topological D-brane categories
Journal of High Energy Physics, 2008.
Xingwu Chen, Valery G. Romanovski, W. Zhang: Linearizability conditions of time-reversible quartic systems having homogeneous nonlinearities
Nonlinear Analysis: Theory, Methods & Applications, 69 (5/6), 1525-1539, 2008.
Mihai Cipu : A computer-aided proof of a conjecture in Euclidean geometry
Computers & Mathematics with Applications, 56 (11), 2814-2818, 2008.
Thomas Cluzeau, Alban Quadrat: Factoring and decomposing a class of linear functional systems
Linear Algebra and its Applications, 428 (1), 324-381, 2008.
S. C. Coutinho : On the classification of simple quadratic derivations over the affine plane
Journal of Algebra, 319 (10), 4249-4274, 2008.
S. C. Coutinho, R. M. Oliveira: An algebraic algorithm for the resolution of singularities of foliations
Applicable Algebra in Engineering, Communication and Computing, 19 (6), 475-493, 2008.
Christian Eder: A new attempt on the F5 Criterion
The Computer Science Journal of Moldova, 16, 4-14, 2008.
Eivind Eriksen, Trond Stølen Gustavsen: Connections on modules over singularities of finite CM representation type
Journal of Pure and Applied Algebra, 212 (7), 1561-1574, 2008.
Raul M. Falcón: 0/1-Polytopes related to Latin squares autotopisms
Proc. of the 6th JMDA 2008, 311-319, 2008.
Raul M. Falcón, Jorge Martín-Morales: The 3-dimensional planar assignment problem and the number of Latin squares related to an autotopism
Proc. of the 11th EACA, 89-92, 2008.
Luis Giraldo, X. Gómez-Mont, P. Mardešić: Flags in zero dimensional complete intersection algebras and indices of real vector fields
Mathematische Zeitschrift, 260 (1), 77-91, 2008.
Luis Giraldo, Antonio J. Pan-Collantes: On the singular scheme of codimension one holomorphic foliations in P^3
International Journal of Mathematics, 1-16, 2008.
Hans-Christian Graf von Bothmer, Wolfgang Ebeling, Xavier Gómez-Mont: An algebraic formula for the index of a vector field on an isolated complete intersection singularity
Annales de l'Institut Fourier, 58 (5), 1761-1783, 2008.
Gert-Martin Greuel, Wolfgang Kunz, Dominik Stoffel, Markus Wedler, Oliver Wienand: An Algebraic Approach for Proving Data Correctness in Arithmetic Data Paths
Lecture Notes in Computer Science, Springer, 5123, 473-486, 2008.
R. V. Gurjar, Vinay Wagh: On the number of generators of the module of derivations and multiplicity of certain rings
Journal of Algebra, 319 (5), 2030-2049, 2008.
Martin Hamm : Die verselle Deformation zyklischer Quotientensingularitäten: Gleichungen und torische Struktur
PhD Thesis (Hamburg University), 2008.
Christopher J. Hillar, Troels Windfeldt: Algebraic Characterization of Uniquely Vertex Colorable Graphs
Journal of Combinatorial Theory, 98 (2), 400-414, 2008.
Kai Hormann, Johannes Zimmer : Exact Modelling of the Phases at the Triple Point of Zirconia
2008.
Z. Hu, V.G. Romanovski, D.S. Shafer: 1:-3 resonant centers on C^2 with homogeneous cubic nonlinearities
Computers & Mathematics with Applications, 56, 1927-1940, 2008.
David Ilsen, E.J. Roebbers, Gert-Martin Greuel: Algebraic and combinatorial algorithms for translinear network synthesis
IEEE Transactions on Circuits and Systems - I: Regular Papers, 55, 3131 - 3144, 2008.
Pål Hermunn Johansen, Magnus Løberg, Ragni Piene: Monoid hypersurfaces
Geometric Modeling and Algebraic Geometry, 55-77, 2008.
Eric Katz, Hannah Markwig, Thomas Markwig: The j-invariant of a plane tropical cubic
Journal of Algebra, 320 (10), 3832-3848, 2008.
George A. Kirkup: Minimal primes over permanental ideals
Transactions of the AMS, 360 (7), 3751-3770, 2008.
Eunjeong Lee, Hyang-Sook Lee, Yoonjin Lee: Eta pairing computation on general divisors over hyperelliptic curves y^2=x^p-x+d
Journal of Symbolic Computation, 43 (6-7), 452-474 , 2008.
Anton Leykin, Jan Verschelde, Ailing Zhao : Higher-Order Deflation for Polynomial Systems with Isolated Singular Solutions
The IMA Vol. in Math. and its Appl., 146, 79-97, 2008.
Christopher Lyons: Large Monodromy for a Family of Surfaces of General Type with p_g=q=1, K^2=3
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Étienne Mann, Ignacio de Gregorio: Mirror fibrations and root stacks of weighted projective spaces
manuscripta mathematica (Springer), 127 (1), 69-80, 2008.
Hossein Movasati, Stefan Reiter: Painlevé VI equations with algebraic solutions and family of curves
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Hossein Movasati, Stefan Reiter: Heun equations coming from geometry
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Ferran Muiños, Francesc Planas-Vilanova: On the Injectivity of Blowing-Up Ring Morphisms
Journal of Algebra, 320 (8), 3365-3380, 2008.
Hajime Nagoya: Quantization of differential systems with the affine Weyl group symmetries of type C^(1)_N
Journal of Mathematical Sciences of the University of Tokyo, 15 (4), 493-519, 2008.
Tetsuo Nakano: On the Moduli Space of Pointed Algebraic Curves of Low Genus II - Rationality
Tokyo Journal of Mathematics, 31 (1), 147-160, 2008.
Luis Narvaez-Macarro : Linearity conditions on the Jacobian ideal and logarithmic-meromorphic comparison for free divisors
Contemporary Mathematics (AMS), 474, 245-269, 2008.
Stavros Argyrios Papadakis: The equations of type II_1 unprojection
Journal of Pure and Applied Algebra, 212 (10), 2194-2208, 2008.
Wilhelm Plesken, Daniel Robertz: Elimination for coefficients of special characteristic polynomials
Experimental Mathematics, 17 (4), 499-510, 2008.
Valery G. Romanovski: Time-Reversibility in 2-Dim Systems
Open Systems and Informational Dynamics, 15, 359-370, 2008.
Yihuang Shen : Tangent cone of numerical semigroup rings with small embedding dimension
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Frank Sottile, Thorsten Theobald : Line problems in nonlinear computational geometry
Contemporary Mathematics, 453, 411-432, 2008.
Jan Stevens : Universal abelian covers of superisolated singularities
Mathematische Nachrichten, 282 (8), 1195-1215, 2008.
Christian Stump : q,t-Fuss-Catalan numbers for finite reflection groups
DMTCS, Proc. of the FPSAC 2008, 2008.
Jukka Tuomela: Kinematic analysis of multibody systems
BIT Numerical Mathematics, 48 (2), 405-421, 2008.
Klaus Wirthmüller: Homological Invariants of Stabilizer States
Quantum Information and Computation, 8 (6-7), 2008.
Feza Arslan, Pinar Mete: Hilbert functions of Gorenstein monomial curves
Proc. of the AMS, 135 (7), 1993-2002, 2007.
Tobias Beck, Josef Schicho : Parametrization of algebraic curves defined by sparse equations
Applicable Algebra in Engineering, Communication and Computing, 18, 127-150, 2007.
Isabel Bermejo, Ignacio García-Marco, Juan José Salazar-González: An algorithm for checking whether the toric ideal of an affine monomial curve is a complete intersection
Journal of Symbolic Computation, 42 (10), 971-991, 2007.
Samuel Boissière, Alessandra Sarti: Counting lines on surfaces
Ann. Scuola Norm. Sup. Pisa Cl. Sci., 6 (1), 39-52, 2007.
Volker Braun, Burt A. Ovrut, Maximilian Kreuzer, Emanuel Scheidegger : Worldsheet instantons and torsion curves. Part B: mirror symmetry
Journal of High Energy Physics, 2007 (10), 23-?, 2007.
Antonio Campillo, José Ignacio Farrán, María-Jesús Pisabarro: Evaluation codes at singular points of algebraic differential equations
Applicable Algebra in Engineering, Communication and Computing, 18 (1-2), 191-203, 2007.
Antonio Campillo, Gert-Martin Greuel, Christoph Lossen : Equisingular Deformations of Plane Curves in Arbitrary Characteristic
Compositio Mathematica, 143 (4), 829-882, 2007.
Antonio Campillo, Gert-Martin Greuel, Christoph Lossen : Equisingular calculations for plane curve singularities
Journal of Symbolic Computation, 42 (1-2), 89-114, 2007.
F. J. Castro-Jiménez, J. M. Ucha, J. Àlvarez Montaner: Localization at hyperplane arrangements: Combinatorics and D-modules
Journal of Algebra, 316 (2), 662-679, 2007.
Eduardo Cattani, Raymond Curran: Restriction of A-discriminants and dual defect toric varieties
Journal of Symbolic Computation, 42 (1-2), 115-135, 2007.
Eduardo Cattani, Alicia Dickenstein: Counting Solutions to Binomial Complete Intersections
Journal of Complexity, 23 (1), 82-107, 2007.
Guillaume Chèze, Grégoire Lecerf: Lifting and recombination techniques for absolute factorization
Journal of Complexity , 23 (3), 380-420, 2007.
A.R. Chouikha, V.G. Romanovski, X. Chen X : Isochronicity of analytic systems via Urabe's criterion
Journal of Physics A: Mathematical and Theoretical, 40 (10), 2313-2327, 2007.
David Cox, Jessica Sidman: Secant varieties of toric varieties
Journal of Pure and Applied Algebra, 209 (3), 651-669, 2007.
Maria Angelica Cueto, Alicia Dickenstein : Some results on inhomogeneous discriminants
Biblioteca de la Revista Matemática Iberoamericana, 2007.
Sławomir Cynk, Sławomir Rams: On a map between two K3 surfaces associated to a net of quadrics
Archiv der Mathematik, 88 (2), 109-122, 2007.
Alberto Damiano, Irene Sabadini, Daniele C. Struppa: Computational methods for the construction of a class of Noetherian operators
Experimental Mathematics, 16 (1) , 41-53, 2007.
James K. Deveney, David R. Finston: Additive group actions with finitely generated invariants
Osaka Journal of Mathematics, 44 (1), 91-98, 2007.
Mathias Drton, Bernd Sturmfels, Seth Sullivant: Algebraic Factor Analysis: Tetrads, Pentads and Beyond
Probability Theory and Related Fields, 138 (3-4), 463-493, 2007.
M'Hammed El Kahoui, Said Rakrak: Structure of Gröbner bases with respect to block orders
Mathematics of Computation, 76 (260), 2181-2187, 2007.
Eivind Eriksen, Trond Stølen Gustavsen: Computing obstructions for existence of connections on modules
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R. M. Falcón, J. Martín-Morales: Gröbner bases and the number of Latin squares related to autotopisms of order ≤ 7
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Stephen E. Fienberg: Expanding the statistical toolkit with algebraic statistics
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Anne Frühbis-Krüger: An Application of Resolution of Singularities: Computing the topological Zeta-function of isolated surface singularities in (C^3,0)
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Eberhard Freitag, Riccardo Salvati Manni : Modular forms for the even unimodular lattice of signature (2,10)
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Eberhard Freitag, Riccardo Salvati Manni: The modular variety of hyperelliptic curves of genus three
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Hans-Christian Graf von Bothmer, Oliver Labs, Josef Schicho, Christiaan van de Woestijne: The Casas-Alvero conjecture for infinitely many degrees
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Edward L. Green, Øyvind Solberg: An algorithmic approach to resolutions
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Martin G. Gulbrandsen : Stack structures on GIT quotients parametrizing hypersurfaces
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Serkan Hosten, Seth Sullivant : The Algebraic Complexity of Maximum Likelihood Estimation for Bivariate Missing Data
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Anders Nedergaard Jensen: A non-regular Gröbner fan
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David Joyner, Amy Ksir, Tony Shashka: Bases for Riemann-Roch spaces of cyclic curves
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Louis H. Kauffman, Simon King, Sostenes Lins: A State Sum Link Invariant of Regular Isotopy
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Simon A. King : Fast Computation of Secondary Invariants
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Simon A. King: Minimal generating sets of non-modular invariant rings of finite groups
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Simon A. King: Ideal Turaev-Viro invariants
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Simon A. King: Fast Computation of Non-Modular Invariant Rings
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Systems & Control Letters, 56 (11-12), 678-684, 2007.
Viktor Levandovskyy: Foreword from the Editor
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Huishi Li : Noncommutative Grobner Bases for Almost Commutative Algebras
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M. Maniatis, A. von Manteuffel, O. Nachtmann : Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM
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Thomas Markwig: Families of Curves and a Lifting Problem for Tropical Varieties
Habilitationsschrift (TU Kaiserslautern), 2007.
Bernd Martin, Hendrik Süß: Milnor Algebras versus Modular Germs for Unimodal Hypersurface Singularities
An. St. Univ. Ovidius Constanta, 15 (1), 111-128, 2007.
Michael Monagan, Roman Pearce : Polynomial Division Using Dynamic Arrays, Heaps, and Packed Exponent Vectors
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Hossein Movasati : On Ramanujan relations between Eisenstein series
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Hossein Movasati: Modular foliations and periods of hypersurfaces
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Hossein Movasati: Mixed Hodge structure of affine hypersurfaces
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Stavros Argyrios Papadakis: Towards a general theory of unprojection
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Stavros Argyrios Papadakis: Some calculations on type II_1 unprojection
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Jens Piontkowski: On the number of cusps of rational cuspidal plane curves
Experimental Mathematics, 16 (2), 251-255, 2007.
Tony J. Puthenpurakal: Ratliff-Rush filtration, regularity and depth of higher associated graded modules: Part I
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Tony J. Puthenpurakal, Fahed Zulfeqarr: Ratliff-Rush filtrations associated with ideals and modules over a Noetherian ring
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Stuart Raby, Akin Wingerter : Can String Theory Predict the Weinberg Angle?
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Valery G Romanovski: Bifurcations of Periodic Points of Some Algebraic Maps
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Valery G. Romanovski: Periodic points of some algebraic maps
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Valery G. Romanovski, X. Chen, Z. Hu: Linearizability of linear systems perturbed by fifth degree homogeneous polynomials
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Diego Ruano: Computing the Feng-Rao distances for codes from order domains
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James Ruffo : A straightening law for the Drinfeld Lagrangian Grassmannian
Proc. of the ISSAC, 323-330, 2007.
Eduardo Sáenz-de-Cabezón: Homological description of Monomial Ideals using Mayer-Vietoris Trees
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Mathias Schulze: A criterion for the logarithmic differential operators to be generated by vector fields
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Caleb McKinley Shor : On the Construction of Codes from an asymptotically good Tower over F_8
Serdica Journal of Computing, 1 (2), 2007.
Pham Tien Son, Ha Huy Vui: Minimizing polynomial functions
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Hirotachi Abo, Chris Peterson: Implementation of Kumar's correspondence
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Hirotachi Abo, Frank-Olaf Schreyer : Exterior algebra methods for the construction of rational surfaces in the projective fourspace
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Tatiana Bandman, Gert-Martin Greuel, Fritz Grunewald, Boris Kunyavskii, Gerhard Pfister, Plotkin Eugene: Engel-like Identities characterizing Finite Solvable Groups
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Enrique Artal Bartolo, Ignacio Luengo Velasco, Alejandro Melle-Hernandez: Superisolated Surface Singularities
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Isabel Bermejo, Philippe Gimenez: Saturation and Castelnuovo-Mumford regularity
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Isabel Bermejo, Philippe Gimenez, Marcel Morales: Castelnuovo-Mumford regularity of projective monomial varieties of codimension two
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Samuel Boissière: Towards the multiplicative behavior of the K-theoretical McKay correspondence
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Markus Brodmann, Peter Schenzel: On varieties of almost minimal degree in small codimension
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Markus Brodmann, Peter Schenzel: Arithmetic properties of projective varieties of almost minimal degree
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Stanislav Bulygin: Generalized Hermitian Codes over GF(2^r)
IEEE Transactions on Information Theory, 52 (10), 4664-4669, 2006.
Yuguo Chen, Ian H. Dinwoodie, Seth Sullivant: Sequential importance sampling for multiway tables
Annals of Statistics, 34 (1), 523-545, 2006.
P. Chrusciel, Gert-Martin Greuel, R. Meinel, J. Szybka: The Ernst equation and ergosurfaces
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S. C. Coutinho, Luis Menasché Schechter: Algebraic solutions of Holomorphic Foliations: an Algorithmic Approach
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Sƚawomir Cynk, Duco van Straten: Infinitesimal deformations of double covers of smooth algebraic varieties
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Mathias Drton : Algebraic Techniques for Gaussian Models
Prague Stochastics (Matfyzpress, Charles University Prague), 81-90, 2006.
Mathias Drton: Computing all roots of the likelihood equations of seemingly unrelated regressions
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Bálint Felszeghy, Balázs Ráth, Lajos Rónyai : The lex game and some applications
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Mitsushi Fujimoto, Masakazu Suzuki, Kazuhiro Yokoyama: On polynomial curves in the affine plane
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Carlos Galindo, M. Sanchis: Evaluation codes and plane valuations
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Vladimir P. Gerdt, Yuri A. Blinkov: On Computing Janet Bases for Degree Compatible Orderings
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Vladimir P. Gerdt, Yuri A. Blinkov, Vladimir V. Mozzhilkin : Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations
SIGMA, 2 (51), 2006.
Tobias Hirsch, Bernd Martin: Deformations with section: Cotangent cohomology, flatness conditions and modular subgerms
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J. William Hoffman, Hao Hao Wang : Curvilinear Base Points, Local Complete Intersection and Kozsul Syzygies in Biprojective Spaces
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Pål Hermunn Johansen: Topics in algebraic geometry and geometric modeling
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Katsiaryna Krupchyk, Jukka Tuomela: The Shapiro-Lopatinskij condition for elliptic boundary value problems
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Oliver Labs: Dessins d'Enfants and Hypersurfaces with Many A_j-Singularities
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Antonio Laface, Luca Ugaglia: On a class of special linear systems of P^3
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Manfred Lehn, Christoph Sorger: La singularité de O'Grady
Journal of Algebraic Geometry, 15 (4), 753-770, 2006.
Anton Leykin, Jan Verschelde, Ailing Zhao : Newton's method with deflation for isolated singularities of polynomial systems
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Christoph Lossen, Gerhard Pfister : Aspects of Gert-Martin Greuel's Mathematical Work
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Laura Felicia Matusevich, Ezra Miller : Combinatorics of rank jumps in simplicial hypergeometric systems
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Laura Felicia Matusevich, Ezra Miller: Combinatorics of rank jumps in simplicial hypergeometric systems
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Hossein Movasati, Stefen Reiter: Hypergeometric series and Hodge cycles of four dimensional cubic hypersurfaces
International Journal of Number Theory, 2 (3), 397-416, 2006.
Uwe Nagel, Tim Römer: Extended degree functions and monomial modules
Transactions of the AMS, 358 (8), 3571-3589, 2006.
James Ruffo, Yuval Sivan, Evgenia Soprunova, Frank Sottile: Experimentation and conjectures in the real Schubert calculus for flag manifolds
Experimental Mathematics, 15 (2), 199-221, 2006.
Evgenia Soprunova, Frank Sottile: Lower Bounds for Real Solutions to Sparse Polynomial Systems
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Jan Stevens : Sextic Surfaces With Ten Triple Points
Lecture Notes of LMS, Cambridge University Press, 2006.
Martijn van Manen: Conflict sets, orthotomics, pedals and billards as canonical relations
Mathematical Proceedings of the Cambridge Philosophical Society, 141 (2), 339-353, 2006.
Marius Vlădoiu: Discrete Polymatroids
An. St. Univ. Ovidius Constanta, 14 (2), 97-120, 2006.
Hao Hao Wang, J. William Hoffman: Curvilinear base points, local complete intersection and Koszul syzygies in biprojective spaces
Transactions of the AMS, 358 (8), 3385-3398, 2006.
Eva Zerz, Viktor Levandovskyy : Algebraic systems theory and computer algebraic methods for some classes of linear control systems
Proc. Math. Theory Networks Systems, 536-541, 2006.
William A. Adkins, J. William Hoffman, Hao Hao Wang : Equations of parametric surfaces with base points via syzygies
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L. C. O. Almeida, S. C. Coutinho: On homogenous minimal involutive varieties
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Frühbis-Krüger Anne, Pfister Gerhard: Some Applications of Resolution of Singularities from a Practical Point of View
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Corina Baciu, Viviana Ene, Gerhard Pfister, Dorin Popescu: Rank two Cohen-Macaulay modules over singularities of type x_1^3+x_2^3+x_3^3+x_4^3
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Tobias Beck, Josef Schicho: Sparse parametrization of plane curves
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Carles Bivià-Ausina: Jacobian ideals and the Newton non-degeneracy condition
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Sonja Breske : Konstruktion von Flächen mit vielen reellen Singularitäten mit Hilfe von Faltungspolynomen
Diploma Thesis (Johannes-Gutenberg-Universität Mainz), 2005.
Enrico Carlini, Fabio Rapallo: The Geometry of Statistical Models for Two-Way Contingency Tables with Fixed Odds Ratios
Rend. Inst. Math. Univ. Triest, 37, 71-84, 2005.
David C. Carothers, G. Edgar Parker, James S. Sochacki, Paul G. Warne: Some properties of solutions to polynomial systems of differential equations
Electronic Journal of Differential Equations, 40, 1-17, 2005.
Luis Abel Castorena: Curves of genus seven that do not satisfy the Gieseker-Petri theorem
Bollettino dell unione matematica italiana. Sezione B: articoli di ricerca matematica, 8 (3), 697-706, 2005.
Luis Abel Castorena: Characteristic frequencies, polynomial-exponential trajectories, and linear exact modeling with multidimensional behaviors
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Eduardo Cattani, Alicia Dickenstein: Introduction to residues and resultants
Algorithms and Computation in Mathematics, 14, 2005.
Sławomir Cynk, Christian Meyer: Geometry and arithmetic of certain double octic Calabi-Yau manifolds
Canadian Mathematical Bulletin, 48 (2), 180-194, 2005.
Javier Fernández de Bobadilla: Answers to some equisingularity questions
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Mike Develin, Francisco Santos, Bernd Sturmfels : On the rank of a tropical matrix
Discrete and Computational Geometry (E. Goodman, J. Pach and E. Welzl, eds.), MSRI Publications, (Cambridge Univ. Press), 52, 213-242, 2005.
Alicia Dickenstein, Ioannis Z. Emiris : Solving polynomial equations: foundations, algorithms, and applications
Algorithms and Computation in Mathematics, 14, 2005.
Marc Dohm, Mohamed Elkadi, André Galligo : µ-Bases of Algebraic Curves and Surfaces
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Markus Eiswirth, Karin Gatermann, Anke Sensse : Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems
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Yong Feng, Xijin Tang: A New Efficient Algorithm for Solving Systems of Multivariate Polynomial Equations
Cryptology ePrint Archive, 312, 2005.
J. Gago-Vargas, M. I. Hartillo-Hermoso, J. M. Ucha-Enríquez: Comparison of theoretical complexities of two methods for computing annihilating ideals of polynomials
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Karin Gatermann, Serkan Hoşten: Computational algebra for bifurcation theory
Journal of Symbolic Computation, 40 (4-5), 1180-1207, 2005.
Karin Gatermann, Matthias Wolfrum: Bernstein's second theorem and Viro's method for sparse polynomial systems in chemistry
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Martin G. Gulbrandsen: A partial resolution of the punctual Hilbert scheme of a nonsingular surface
Mathematica Scandinavica, 96 (1), 5-21, 2005.
Mohammad A. A. Hamad, Fouad S. Ibrahim, Mohammad A. Mansour: Lie-group analysis of radiative and magnetic field effects on free convection and mass transfer flow past a semi-infinite vertical flat plate
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Serkan Hoşten, Amit Khetan, Bernd Sturmfels: Solving the likelihood equations
Foundations of Computational Mathematics, 5 (4), 389-407, 2005.
Pål Hermunn Johansen: The Geometry of the Tangent Developable
Computational Methods for Algebraic Spline Surfaces, 95-106, 2005.
Tomaž Košira, B. A. Sethuraman: A Groebner basis for the 2 times 2 determinantal ideal mod t^2
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Oliver Labs : A Sextic with 35 Cusps
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Martin Lotz: On numerical invariants in algebraic complexity theory
PhD Thesis (University Paderborn), 2005.
I. Luengo-Velasco, Alejandro Melle-Hernández, A. Némethi: Links and analytic invariants of superisolated singularities
Journal of Algebraic Geometry, 14 (3), 543-565, 2005.
Paulo A. Machado Fonseca, Israel Vainsencher: Les degrés des variétés des matrices nilpotentes
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Sihem Mesnager: Test of epimorphism for finitely generated morphisms between affine algebras over computational rings
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Hossein Movasati : Differential modular forms, Elliptic curves and Ramanujan foliation
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Anke Sensse: Convex and toric geometry to analyze complex dynamics in chemical reaction systems
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Namrata Shekhar, Priyank Kalla, Florian Enescu, Sivaram Gopalakrishnan : Exploiting Vanishing Polynomials for Equivalence Verification of Fixed-Size Arithmetic Datapaths
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Namrata Shekhar, Priyank Kalla, Florian Enescu, Sivaram Gopalakrishnan: Equivalence Verification of Polynomial Datapaths with Fixed-Size Bit-Vectors using finite Ring Algebra
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Michael Stillman : Tools for computing primary decompositions and applications to ideals associated to Bayesian networks
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Frühbis-Krüger Anne: Partial Standard Bases as a Tool for Studying Families of Singularities
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Frank Bauer : An Alternative Approach to the Oblique Derivative Problem in Potential Theory
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Arnaud Bodin: Computation of Milnor numbers and critical values at infinity
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René Brandenberg, Thorsten Theobald: Algebraic methods for computing smallest enclosing and circumscribing cylinders of simplices
Applicable Algebra in Engineering, Communication and Computing, 14 (6), 2004.
F. J. Castro-Jiménez, J. M. Ucha: On the computation of Bernstein-Sato ideals
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Juan Elias : Depth of higher associated graded rings
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Béla Finta : Finding Roots of nonlinear System of Equations on a Domain
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Luis David Garcia-Puente: Algebraic geometry of Bayesian networks
PhD Thesis (Blacksburg University, Virginia), 2004.
Antonio Laface, Luca Ugaglia: A counterexample to a conjecture on linear systems on P^3
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Jérôme Lebrun, Ivan Selesnick: Gröbner bases and wavelet design
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Daniel P. McAllaster: Some Algorithms in Algebraic Geometry
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Sihem Mesnager: Construction of the integral closure of an affine domain in a finite field extension of its quotient field
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Tatsuji Mori, Tetsuo Nakano: On the Moduli Space of Pointed Algebraic Curves of Low Genus - A Computational Approach
Tokyo Journal of Mathematics, 27 (1), 239-253, 2004.
Shun-Ichiro Okuda: Kernels of derivations in positive characteristic
Hiroshima Mathematical Journal, 34 (1), 1-19, 2004.
Hyungju Park: Symbolic computation and signal processing
Journal of Symbolic Computation, 37 (2), 209-226, 2004.
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.
Shustin Shustin, Eric Westenberger: Projective hypersurfaces with many singularities of prescribed types
Journal of the LMS, 70 (3), 609-624, 2004.
Jan Stevens : Some adjacencies to cusp singularities
Real and Complex Singularities. Contemporary Mathematics, Amer. Math. Soc., 354, 291-300, 2004.
Irena Swanson: On the embedded primes of the Mayr-Meyer ideals
Journal of Algebra, 275 (1), 143-190, 2004.
Johannes Zimmer: Stored energy functions for phase transitions in crystals
Archive for Rational Mechanics and Analysis, 172 (2), 191-212, 2004.
Francois Anton, Darka Mioc: A certified predicate for maintaining the topology of the Voronoi diagram for conics
Proc. X Encuentros de Geometria Computacional, 2003.
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.
Thomas Bayer: Algorithms for the Computation of Moduli Spaces for Semiquasihomogeneous Singularities
Revista Matemática Complutense , 16 (1), 103-129, 2003.
Markus Brodmann, Peter Schenzel: On projective curves of maximal regularity
Mathematische Zeitschrift, 244 (2), 271-289, 2003.
Winfried Bruns, Wolmer V. Vasconcelos: Minors of symmetric and exterior powers
Journal of Pure and Applied Algebra, 179 (3), 235-240, 2003.
Igor Burban, Hans-Georg Freiermuth : Geometrical properties of sections of Buchsbaum-Rim sheaves
2003.
Massimo Caboara, C. Traverso: Efficient algorithms for basic module operations
2003.
Arthur D. Chtcherba : A new Sylvester-type Resultant Method based on the Dixon-B�zout Formulation
2003.
A. Collino, Stefan Müller-Stach, Shuji Saito: On K1 and K2 of algebraic surfaces
K-Theory, 30 (1), 37-69, 2003.
Nicolas T. Courtois, Magnus Daum, Patrick Felke : On the Security of HFE, HFEv- and Quartz
Lecture Notes in Computer Science, 2567, 337-350, 2003.
James Damon: On the Legacy of Free Divisors II: Free* Divisors and Complete Intersections
Moscow Mathematical Journal, 3 (2), 361-395, 2003.
Ruchira S. Datta : Using computer algebra to find Nash equilibria
Proc. of the ISSAC, 74-79, 2003.
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.
Gert-Martin Greuel: A Computer Algebra Solution to a Problem in Finite groups
Revista Matematica Iberoamericana, 19 (2), 413-424, 2003.
Agnes Eileen Heydtmann: Sudan-decoding generalized geometric Goppa codes
Finite Fields and Their Applications, 9 (3), 267-285, 2003.
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.
Viatcheslav Kharlamov, Frank Sottile : Maximally inflected real rational curves
Moscow Mathematics Journal, 3 (3), 947-987, 2003.
Shrawan Kumar, Jesper Funch Thomsen: A conjectural generalization of the n! result to arbitrary groups
Transformation Groups, 8 (1), 69-94, 2003.
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.
Anton Leykin: Algorithms in computational algebraic analysis
PhD Thesis (Minnesota University), 2003.
Christoph Lossen : Singular: A Computer Algebra System
Computing in Science and Engineering, 5 (4), 45-55, 2003.
Bernd Martin : Modular Deformations and Space Curve Singularities
Revista Matematica Iberoamericana, 19 (2), 613-621, 2003.
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.
Gerhard Pfister : A Problem in Group Theory Solved by Computer Algebra
Proc. of the CCASCA, Sinaia 2002, Kluwer Academic Publishers, 217-223, 2003.
F. Leon Pritchard: On implicit systems of differential equations
Journal of Differential Equations, 194 (2), 328-363, 2003.
Mathias Schulze : Monodromy of Hypersurface Singularities
Acta Applicandae Mathematicae, 75 (1-3), 3-13, 2003.
Christian Sevenheck : Lagrange-Singularitäten
Dissertation (Johannes-Gutenberg-Universität Mainz), 2003.
Frank Sottile: Toric ideals, real toric varieties, and the moment map
Proc. of AGGM, Vilnius, Lithuania. Contemporary Mathemathics, 334, 225-240, 2003.
Jan Stevens : Sextic surfaces with ten triple points
2003.
Irena Swanson: The minimal components of the Mayr-Meyer ideals
Journal of Algebra , 267 (1), 137-155, 2003.
Susumu Tanabé: Combinatorial aspects of the mixed Hodge structure
RIMS Kokyuroku "New aspects of the singularity theory", 2003.
T. Theobald : New algebraic methods in computational geometry
Habilitationsschrift, 2003.
Martijn van Manen: The geometry of conflict sets
PhD Thesis (Utrecht University, Netherlands), 2003.
Ralf-Philipp Weinmann : Evaluating algebraic attacks on the AES
Diploma Thesis (Technische Universität Darmstadt), 2003.
Teijo Arponen : The complete form of a differential algebraic equation
2002.
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.
Arnaud Bodin : Non-reality and non-connectivity of complex polynomials
Comptes Rendus Mathematique, 335 (12), 1039-1042, 2002.
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.
Patrick Dondl : Modeling and Analysis of Non-Diffusive Structural Phase Transitions in Crystals
Diploma Thesis (Bath University, UK), 2002.
Jean Charles Faugère: A new efficient algorithm for computing Groebner bases without reduction to zero (F5)
Proc. of the ISSAC'02, 75-83, 2002.
Eberhard Freitag : A graded algebra related to cubic surfaces
Kyushu Journal of Mathematics, 56 (2), 299-312, 2002.
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.
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.
Gert-Martin Greuel, Gerhard Pfister: Computer Algebra and Finite Groups
Proc. of the FICMS, Beijing 2002. World Scientific, 4-14, 2002.
M. I. Hartillo, J. M. Ucha: A Computational Introduction to the Weyl Algebra and D-modules
2002.
Grégoire Lecerf: Quadratic Newton iteration for systems with multiplicity
Foundations of Computational Mathematics, 2 (3), 247-293, 2002.
Martijn van Manen : Applications of canonical relations in generic differential geometry
2002.
Bernd Martin : Algorithmic Computation of Flattenings and of Modular Deformations
Journal of Symbolic Computation, 34 (3), 199-212, 2002.
Michel Van den Bergh: Non-commutative crepant resolutions
The legacy of Niels Henrik Abel, Springer, 749-770, 2002.
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.
S. C. Coutinho, Bruno F. M. Ribeiro: On holomorphic foliations without algebraic solutions
Experimental Mathematics, 10, 529-536, 2001.
Anne Frühbis-Krüger: Computing moduli spaces for space curve singularities
Journal of Pure and Applied Algebra, 164 (1-2), 165-178, 2001.
Ryutaroh Matsumoto: Computing the radical of an ideal in positive characteristic
Journal of Symbolic Computation, 32 (3), 263-271, 2001.
Ivan W. Selesnick: Smooth wavelet tight frames with zero moments
Applied and Computational Harmonic Analysis, 10 (2), 163-181, 2001.
Doris Altmann, Klaus Altmann : Estimating Vaccine Coverage by Using Computer Algebra
IMA Journal of Mathematics Applied in Medicine and Biology, 17, 137-146, 2000.
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.
Gert-Martin Greuel: Computer Algebra and Algebraic Geometry - Achievements and Perspectives
Journal of Symbolic Computation, 30 (3), 253-290, 2000.
Anna Guerrieri, Irena Swanson: Jacobian ideals of trilinear forms: an application of 1-genericity
Journal of Algebra, 226 (1), 410-435, 2000.
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.
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.
N. P. Kirk: Computational aspects of classifying singularities
LMS Journal of Computation and Mathematics, 3, 207-228, 2000.
I.W. Selesnick : Balanced multiwavelet bases based on symmetric FIR filters
IEEE Trans. Signal Proc., 48, 184-191, 2000.
Frank Sottile : Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro
Experimental Mathematics, 9 (2), 161-182, 2000.
Frank Sottile : Some real and unreal enumerative geometry for flag manifolds
Michigan Math Journal, 48, 573-592, 2000.
Isabel Bermejo, Philippe Gimenez: On Castelnuovo-Mumford regularity of projective curves
Proc. of the AMS, 128 (5), 1293-1299, 1999.
Anne Frühbis-Krüger: Classification of Simple Space Curve Singularities
Communications in Algebra, 27 (8), 3993-4013, 1999.
Alejandro Melle-Hernández: Euler characteristic of the Milnor fibre of plane singularities
Proc. of the AMS, 127 (9), 2653-2655, 1999.
Stephen F. Siegel, Sarah J. Witherspoon: The Hochschild cohomology ring of a group algebra
Proc. of the LMS, 79 (1), 131-157, 1999.
Massimo Caboara: Optimization of basic algorithms in Commutative Algebra
PhD Thesis (Pisa University), 1998.
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.
Hyungju Park : Algorithms for Determining Birationality of Parametrization of Affine Curves
1998.
Mesut Şahin: Complete intersection monomial curves and non-decreasing Hilbert functions
PhD Thesis (Bilkent University, Ankara), 2008.
Xingwu Chen: Linearizability conditions of a time-reversible quartic-like system.
J. Gin\'e, V.G. Romanovski: Linearizability conditions for Lotka--Volterra planar complex cubic systems
J. Phys. A: Math. Theor., 42, 225206-225221.
Jaume Gine: Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities.
Eduardo Sáenz-de-Cabezón: Computing the support of monomial iterated mapping cones
Journal of Symbolic Computation, 45 (10), 953-964.

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