Publications

• Introductory Textbooks
• Overview Articles
• Manual, Tutorial and Reference Card for SINGULAR
• Information on Implemented Algorithms and Libraries
• Series: ZCA Reports on Computer Algebra
• Books Providing SINGULAR Examples
• Some Further Publications Referring to SINGULAR
• How to cite SINGULAR

Introductory Textbooks

• W. Decker, C. Lossen: Computing in Algebraic Geometry - A Quick Start using Singular. ACM 16, Springer-Verlag 2005/06.
• G.-M. Greuel, G. Pfister: A Singular Introduction to Commutative Algebra (with contributions by O. Bachmann, C. Lossen, and H. Schönemann). Springer-Verlag 2002. Second edition appeared in 2007.
• M. Sala, T. Mora, L. Perret, S. Sakata, C. Traverso (Editors) Gröbner Bases, Coding, and Cryptography. 2009, XVI, 430 pages, Hardcover, ISBN: 978-3-540-93805-7.

Overview Articles

• G.-M. Greuel, G. Pfister: SINGULAR and Applications. Jahresbericht der DMV 108 (2006), 167-196.
• C. Lossen, H. Schönemann: 21 Years of Singular Experiments in Mathematics. In: C. Lossen and G. Pfister (eds.), Singularities and Computer Algebra. Lecture Notes of LMS, Cambridge University Press, to appear (2005/06).
• C. Lossen: Singular: A Computer Algebra System. CISE 5, No. 4 (2003), 45-55.
• G.-M. Greuel, G. Pfister, H. 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. (2001), 227-233.
• G.-M. Greuel: Applications of Computer Algebra to Algebraic Geometry, Singularity Theory and Symbolic-Numerical Solving. In: European Congeress of Mathematicians, Barcelona, July 10-14, 2000, Vol. II. (2000), 169-188. HTML Version.
• G.-M. Greuel: Computer Algebra and Algebraic Geometry - Achievements and Perspectives. Journ. Symb. Comp. 30,3 (2000), 253-290. HTML Version.
• G.-M. Greuel, G. Pfister: Gröbner bases and algebraic geometry. In: B. Buchberger and F. Winkler: Gröbner Bases and Applications. LNS 251 , CUP (1998), 109-143.
• G.-M. Greuel: Description of Singular: A Computer Algebra System for Singularity Theory, Algebraic Geometry and Commutative Algebra. Euromath Bulletin 2 (1996), 161-172.

Manual, Tutorial and Reference Card for SINGULAR

• Singular Manual: for latest version (Postscript , Dvi , HTML)
• Singular Manual: for version 2( HTML)
• Reference Card (Postscript , Pdf).

Information on Implemented Algorithms and Libraries

• M. Brickenstein, A. Dreyer, PolyBoRi: A framework for Gröbner basis computations with Boolean polynomials. Journal of Symbolic Computation, Volume 44, Issue 9, September 2009, pp. 1326–1345.
• A. Frühbis-Krüger, G. Pfister: Algorithmic Resolution of Singularities. In: C. Lossen and G. Pfister (eds.), Singularities and Computer Algebra. Lecture Notes of LMS, Cambridge University Press, to appear (2005/06).
• M. Brickenstein: Slimgb: Gröbner bases with slim polynomials. Reports on Computer Algebra 35, ZCA, University of Kaiserslautern (2005).
• E.A. Tobis: Libraries for Counting Real Roots. Reports on Computer Algebra 34, ZCA, University of Kaiserslautern (2005).
• V. Levandovskyy: Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation. Doctoral Thesis, University of Kaiserslautern (2005).
• A. Frühbis-Krüger, G. Pfister: Some Applications of Resolution of Singularities from a Practical Point of View. In: Proceedings of the Conference Computational Commutative and Non-commutative Algebraic Geometry, Chisinau 2004, NATO Science Series III, Computer and Systems Sciences 196 (2005), 104-117.
• M. Schulze: Good bases for tame polynomials. J. Symb. Comp. 39,1 (2005), 103-126.
• A. Frühbis-Krüger, G. Pfister: Practical Aspects of Algorithmic Resolution of Singularities. Reports on Computer Algebra 33, ZCA, University of Kaiserslautern (2004).
• A. Frühbis-Krüger: Partial Standard Bases as a Tool for Studying Families of Singularities. J. Symb. Comp. 38, 1191-1205 (2004).
• M. Schulze: A normal form algorithm for the Brieskorn lattice. J. Symb. Comp. 38,4 (2004), 1207-1225.
• V. Levandovskyy, H. Schönemann: PLURAL - a Computer Algebra System for Noncommutative Polynomial Algebras. In: M.Bronstein (ed.): Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2003), Philadelphia, USA. ACM Press (2003).
• V. Levandovskyy: PBW Bases, Non-Degeneracy Conditions and Applications. In: Buchweitz, R.-O. and Lenzing, H. (eds.): Proceedings of the ICRA X conference, Toronto, Canada. Fields Institute (2003).
• I.M. Sulandra: Über Gröbnerwalkalgorithmen. PhD Thesis, Universität des Saarlandes (2003).
• A. Frühbis-Krüger, K. Krüger, H. Schönemann: Dynamic Modules in Singular. Reports on Computer Algebra 32, ZCA, University of Kaiserslautern (2003).
• T. Hirsch: Computing the integral closure of an ideal using its Rees algebra. Prepr. BTU Cottbus M-02/2002 (2002).
• H. Schönemann: Data representations in the computer algebra system Singular. In: Workshop on Applications of Commutative Algebra, Catania. (2002).
• V. Levandovskyy: On Gröbner bases for noncommutative G-algebras. In: Proceedings of the 8th Rhine Workshop on Computer Algebra, Mannheim, Germany. (2002).
• F. Hernando: Computation of the Alexander polynomial of a plane curve singularity and an implementation in Singular. Master Thesis, University of Kaiserslautern (2002).
• M. Schulze: The differential structure of the Brieskorn lattice. In: A.M. Cohen et al.: Mathematical Software - ICMS 2002. World Scientific (2002).
• M. Schulze: Algorithmic Gauss-Manin Connection. Dissertation, Universität Kaiserslautern (2002).
• M. Schulze, J.H.M. Steenbrink: Computing Hodge-theoretic invariants of singularities. In: D. Siersma et al.: New Developments in Singularity Theory. NATO Science Series , Kluwer (2001), 235-255.
• G.-M. Greuel, C. Lossen, M. Schulze: Three Algorithms in Algebraic Geometry, Coding Theory, and Singularity Theory. In: C. Ciliberto et al: Application of Algebraic Geometry to Coding Theory, Physics and Computation, Proceedings. Kluwer (2001), 161-194. HTML Version.
• V.P. Gerdt, Y.A. Blinkov, D.A. Yanovich: Construction of Janet bases I: Monomial bases. In: E.\ Ghanza et al (eds.), Computer Algebra in Scientific Computing -- CASC 2001, 233--247. Springer-Verlag (2001).
• V.P. Gerdt, Y.A. Blinkov, D.A. Yanovich: Construction of Janet bases II: Polynomial bases. In: E.\ Ghanza et al (eds.), Computer Algebra in Scientific Computing -- CASC 2001, 233--247. Springer-Verlag (2001).
• M. Schulze: Algorithms for the Gauss-Manin connection. J. Symb. Comp. 23,5 (2001), 549-564.
• H. Schönemann: Polynomials in Factory and Singular. In: Nikolaus-Konferenz Aachen. (1999).
• T. Bayer: Computation of moduli spaces for semiquasihomogenous singularities and an implementation in Singular. Diplomarbeit, University of Kaiserslautern (2000).
• T. Siebert: Recursive Computation of Free Resolutions and a Generalized Koszul Complex. Reports on Computer Algebra 28, ZCA, University of Kaiserslautern (2000). HTML Version.
• M. Lamm: Hamburger-Noether Entwicklung von Kurvensingularitäten. Diplomarbeit, University of Kaiserslautern (1999).
• M. Schulze: Computation of the Monodromy of an Isolated Hypersurface Singularity. Diplomarbeit, Universität Kaiserslautern (1999).
• M. Wenk: Resultantenmethoden zur Lösung algebraischer Gleichungssysteme implementiert in Singular. Diplomarbeit, University of Kaiserslautern (1999).
• C. Theis: Der Buchberger-Algorithmus für torische Ideale und seine Anwendung in der ganzzahligen Optimierung. Diplomarbeit, Universität des Saarlandes (1999).
• D. Hillebrand: Triangulierung nulldimensionaler Ideale -- Implementierung und Vergleich zweier Algorithmen. Diplomarbeit, Universität Dortmund (1999).
• O. Bachmann and H. Schönemann: Monomial Representations for Groebner Basis Computations. Reports on Computer Algebra 18, ZCA, University of Kaiserslautern (1998; appeared also in: ISSAC 1998). HTML Version.
• W. Decker, G.-M. Greuel, G. Pfister, T. De Jong: The normalisation: a new algorithm, implementation and comparisons. In: Proc. EUROCONFERENCE Computational Methods for Representations of Groups and Algebras (1.4.-5.4.1997). Birkhäuser (1998).
• W. Decker, G.-M. Greuel, G. Pfister: Primary decomposition: algorithms and comparisons. In: G.-M. Greuel, B.H. Matzat, G. Hiss: Algorithmic Algebra and Number Theory. Springer Verlag, Heidelberg (1998), 187-220.
• B. Martin: Computing versal deformations with singular. In: Algorithmic Algebra ans Number Theory, Springer-Verlag, 283-294 (1998).
• O. Bachmann, S. Gray, and H. Schönemann: MP Prototype Specification. Reports on Computer Algebra 12, ZCA, University of Kaiserslautern (1997). HTML Version.
• K. Krüger: Klassifikation von Hyperflächensingularitäten. Diplomarbeit, University of Kaiserslautern (1997).
• T. Wichmann: Der FGLM Algorithmus - verallgemeinert und implementiert in Singular. Diplomarbeit, University of Kaiserslautern (1997).
• T. Siebert: On strategies and implementations for computations of free resolutions. Reports on Computer Algebra 8, ZCA, University of Kaiserslautern (1996). HTML Version.
• A.E. Heydtmann: Generating Invariant Rings of Finite Groups. Diplomarbeit, Universität des Saarlandes (1999).
• H. Grassmann, G.-M. Greuel, B. Martin, W. Neumann, G. Pfister, W. Pohl, H. Schönemann, T. Siebert: On an implementation of standard bases and syzygies in Singular. AAECC 7 (1996), 235-149.
• H. Schönemann: Algorithms in Singular. Reports on Computer Algebra 2, ZCA, University of Kaiserslautern (1996). HTML Version.
• G.-M. Greuel, G. Pfister: Advances and improvements in the theory of standard bases and syzygies. Arch. Math. 66 (1996), 163-176.
• H. Grassmann, G.-M. Greuel, B. Martin, W. Neumann, G. Pfister, W. Pohl, H. Schönemann, T. Siebert: Standard bases, syzygies and their implementation in Singular. In: Beiträge zur angewandten Analysis und Informatik. Shaker, Aachen (1994), 69-96.

Books Providing SINGULAR Examples

• V. Romanovski and D. Shafer: The Center and Cyclicity Problems. A Computational Algebra Approach, Birkhäuser (2008)
• G.-M. Greuel, C. Lossen, E. Shustin: Introduction to Singularities and Deformations. Springer Verlag, Berlin, Heidelberg, New York (2006), 476 pages.
• W. Decker, C. Lossen: Computing in Algebraic Geometry - A Quick Start using Singular. ACM 16, Springer-Verlag 2005/06.
• B. Sturmfels: Solving Systems of Polynomial Equations. CBMS Regional Conference Series in Mathematics, AMS, Providence, RI, 2002.
• G.-M. Greuel, G. Pfister: A Singular Introduction to Commutative Algebra (with contributions by O. Bachmann, C. Lossen, and H. Schönemann). Springer-Verlag 2002.
• D. Cox, J. Little, D. O'Shea: Using Algebraic Geometry. Springer-Verlag 1998.
• D. Cox, J. Little, D. O'Shea: Ideals, Varieties, and Algorithms. Springer-Verlag 1997.

Some Further Publications Referring to SINGULAR

• G. V. Bard: Algebraic Cryptanalysis. Springer Publishing Company, Incorporated, 2009, ISBN 978-0-387-88756-2.
• S. Bulygin, R. Pellikaan: Decoding linear error-correcting codes up to half the minimum distance with Gröbner bases. In Sala, M.; Mora, T.; Perret, L.; Sakata, S.; Traverso, C. (Eds.) Gröbner Bases, Coding, and Cryptography (RISC Book Series, Springer), pp.361-365 (2009).
• R. Matsumoto. Radical Computation for Small Characteristics. In Sala, M.; Mora, T.; Perret, L.; Sakata, S.; Traverso, C. (Eds.) Gröbner Bases, Coding, and Cryptography (RISC Book Series, Springer), pp.427-430 (2009).
• E. Guerrini, E. Orsini, M. Simonetti. Gröbner Bases for the Distance Distribution of Systematic Codes. In Sala, M.; Mora, T.; Perret, L.; Sakata, S.; Traverso, C. (Eds.) Gröbner Bases, Coding, and Cryptography (RISC Book Series, Springer), pp.367-372 (2009).
• M. Borges-Quintana, M.A. Borges-Trenard, E. Martinez-Moro. An Application of Möller's Algorithm to Coding Theory. In Sala, M.; Mora, T.; Perret, L.; Sakata, S.; Traverso, C. (Eds.) Gröbner Bases, Coding, and Cryptography (RISC Book Series, Springer), pp.379-384 (2009).
• I. Karolkiewicz, A. Nowel, Z. Szafraniec: An algebraic formula for the intersection number of a polynomial immersion,
• K. Wirthmüller: Homological Invariants of Stabilizer States. Quantum Information and Computation, Vol. 8, No. 6 & 7 (2008) 0595-0621 Available at http://www.rintonpress.com/journals/qiconline.html and here
• I. Karolkiewicz, A. Nowel, Z. Szafraniec. An algebraic formula for the intersection number of a polynomial immersion Available at http://arxiv.org/abs/0807.1838
• X. Chen, V. G. Romanovski and W. Zhang, Linearizability conditions of time-reversible quartic systems having homogeneous nonlinearities, Nonlinear Analysis: Theory, Methods and Applications 69, no. 5-6, (2008) 1525-1539.
• F. Kubler, K.H. Schmedders: Competitive Equilibria in Semi-Algebraic Economies PIER Working Paper No. 07-013 (March 22, 2007). Available at SSRN: http://ssrn.com/abstract=976890
• E. Cattani and A. Dickenstein: Counting Solutions to Binomial Complete Intersections. Journal of Complexity 23, Issue 1, Feb. 2007, 82-107. Available at http://arxiv.org/abs/math.AC/0510520
• R. Blanco: Complexity of Villamayor's algorithm in the non exceptional monomial case. to appear in International Journal of Mathematics Available at http://arxiv.org/abs/0704.3416
• I. Bermejo, I. Garcia-Marco and J.J. Salazar-Gonzalez: An algorithm for checking whether the toric ideal of an affine monomial curve is a complete intersection, J. Symbolic Comput. 42 (2007) 971--999
• A.R. Chouikha, V.G. Romanovski and X. Chen X. Isochronicity of analytic systems via Urabe's criterion, Journal of Physics A: Mathematical and Theoretical, 40, (2007) 2313-2327
• V.G. Romanovski, X. Chen and Z. Hu, Linearizability of linear systems perturbed by fifth degree homogeneous polynomials, Journal of Physics A: Mathematical and Theoretical 40, no 22, (2007) 5905-5919.
• I. Bermejo, Ph. Gimenez and M. Morales: Castelnuovo-Mumford regularity of projective monomial varieties of codimension 2, J. Symbolic Comput. 41 (2006) 1105--1124
• I. Bermejo and Ph. Gimenez: Saturation and Castelnuovo-Mumford regularity, J. Algebra 303 (2006) 592--617
• P. Chrusciel, G.-M. Greuel, R. Meinel, S. Szybka: The Ernst equation and ergosurfaces. Preprint, http://arxiv.org/abs/gr-qc/0603041, (2006), 1-23. To appear in Classical and Quantum Gravity.
• S. C. Coutinho and L. Menasche Schechter: Algebraic solutions of Holomorphic Foliations: an Algorithmic Approach, Journal of Symbolic Computation vol. 41 (2006), 603--618.
• V. P. Gerdt, Y. A. Blinkov and V. V. Mozzhilkin: Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations, SIGMA 2 (2006), 051, 26 pages
• J. F. de Bobadilla: Answers to some equisingularity questions. Inventiones Mathematicae, 161(3): 657-675 (2005).
• K. Gatermann, S. Hosten: Computational algebra for bifurcation theory. Journal of Symbolic Computation, 40(4-5): 1180- 1207 (2005).
• J. Stevens: Sextic Surfaces With Ten Triple Points. In: C. Lossen and G. Pfister (eds.), Singularities and Computer Algebra. Lecture Notes of LMS, Cambridge University Press, to appear (2005/06).
• J. Fernandez de Bobadilla: Answers to some equisingularity questions. Invent. Math. 161, no. 3, 657-675 (2005).
• L. C. O. Almeida and S. C. Coutinho: On homogenous minimal involutive varieties, LMS J.Comput. Math. vol. 8 (2005) 301--315.
• M. Brodmann, P. Schenzel: Arithmetic properties of projective varieties of almost minimal degree. Preprint Universität Zürich (2005).
• T. Kosir, B.A. Sethuraman: A Groebner basis for the 2 x 2 determinantal ideal mod t². Journal of Algebra 292, 138--153 (2005).
• J. Ruffo, Y. Sivan, E. Soprunova, F. Sottile: Experimentation and conjectures in the real Schubert calculus for flag manifolds. Preprint arXiv:math.AG/0507377 (2005).
• E. Soprunova, F. Sottile: Lower Bounds for Real Solutions to Sparse Polynomial Systems. Advances in Mathematics, to appear. arXiv:math.AG/0409504 (2004).
• O. Labs, D. van Straten: A septic with 99 real nodes. Preprint arXiv:math.AG/0409348 (2004).
• J. Stevens: Some adjacencies to cusp singularities. In: Real and Complex Singularities. Contemporary Mathematics 354, American Mathematical Society, 291-300 (2004).
• I. Luengo-Velasco, A. Melle-Hernandez, A. Nemethi: Links and analytic invariants of superisolated singularities. Preprint arXiv:math.AG/0312416 (2003).
• J.W. Hoffman, H.H. Wang: Curvilinear Base Points, Local Complete Intersection and Kozsul Syzygies in Biprojective Spaces. Preprint arXiv:math.AG/0304118 (2003).
• G. Megyesi, G., F. Sottile, T. Theobald: Common transversals and tangents to two lines and two quadrics in P³. Discrete and Computational Geometry 30, 543--571 (2003).
• F. Sottile: Toric ideals, real toric varieties, and the moment map. In: R. Goldman, R. Krasuaskas (eds.), Topics in Algebraic Geometry and Geometric Modeling. (Proceedings of AGGM, Vilnius, Lithuania.) Contemp. Math. 334, 225-240 (2003).
• T. Hirsch, B. Martin: Deformations with section: Cotangent cohomology, flatness and modular subspaces. Preprint arXiv:math.CV/0306281 (2003).
• N. Courtois, M. Daum, P. Felke: On the Security of HFE, HFEv- and Quartz. In: PKC 2003, LNCS 2567, Springer, pp. 337-350 (2003).
• R.S. Datta: Using computer algebra to find Nash equilibria. In: Proc. of Int. Symp. on Symbolic and Algebraic Computation (ISSAC), pp. 74-79. ACM, 2003.
• M. Brodmann, P. Schenzel: On projective curves of maximal regularity. Math. Zeitschrift 244, 271-289 (2003).
• T. Theobald: New algebraic methods in computational geometry. Habilitationsschrift 2003.
• B. Martin: Modular Deformations and Space Curve Singularities. Rev. Mat. Iberoamericana 19, no. 2, 613-621 (2003).
• V. Kharlamov, F. Sottile: Maximally inflected real rational curves. Moscow Mathematics Journal 3, no. 3, 947-987, 1199-1200 (2003).
• T. Bandman, G.-M.Greuel, F. Grunewald, B. Kunyavskii, G. Pfister, E. Plotkin: Engel-Like Identities Characterizing Finite Solvable Groups. Preprint, http://arXiv.org/abs/math.GR/0303165 (2003).
• G. Pfister: A Problem in Group Theory Solved by Computer Algebra. In: Proceedings of the Conference Commutative Algebra, Singularities and Computer Algebra, Sinaia 2002, Kluwer Academic Publishers 2003, 217-223.
• E. Freitag: A graded algebra related to cubic surfaces. Kyushu Journal of. Math. 56, No. 2, 299-312 (2002).
• G.-M. Greuel: A Computer Algebra Solution to a Problem in Finite groups. Revista Matematica Iberoamericana (2002).
• G.-M. Greuel, G. Pfister: Computer Algebra and Finite Groups. In: A. Cohen, X.-S. Gao, N. Takayama: Proceedings of the First International Congress of Mathematical Software, Beijing 2002. World Scientific (2002).
• I. Bermejo and Ph. Gimenez: Computing the Castelnuovo-Mumford regularity of some subschemes of P^n using quotients of monomial ideals, J. Pure Applied Algebra 164 (2001) 23--33
• A. Frühbis-Krüger: Construction of Moduli Spaces for Space Curve Singularities. JPAA 164, 165-178 (2001).
• I.W. Selesnick: Balanced multiwavelet bases based on symmetric FIR filters. IEEE Trans. Signal Proc. 48, 184-191 (2000).
• D. Altmann, K. Altmann: Estimating vaccine coverage by using computer algebra. IMA Journal of Mathematics Applied in Medicine and Biology 17, 137-146 (2000).
• I. Bermejo and Ph. Gimenez: On Castelnuovo-Mumford regularity of projective curves<, Proc. Amer. Math. Soc. 128 (2000) 1293--1299
• F. Sottile: Some real and unreal enumerative geometry for flag manifolds, Michigan Math Journal 48, 573-592 (2000).
• F. Sottile: Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro. Experimental Mathematics 9, Number 2, 161-182 (2000).
• A. Frühbis-Krüger: Classification of Simple Space Curve Singularities. Comm. in Alg. 27 (8), 3993-4013 (1999).
• B. Huber, F. Sottile, B. Sturmfels: Numerical Schubert calculus. J. Symb. Comp. 26, 767-788 (1998).

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