Publications of Werner M. Seiler

This page contains a list of all my publications to date (well, up to the date given in the bottom line ;-). For faster access, I have organised the list into the following groups:

Books * Journal Articles * Proceedings * Preprints * Editorial Activities

Clicking on the title of a paper opens a page with additional information. Usually this includes a brief description of the content (or some other comments) and in most cases you can download a PDF version of the paper (compressed with gzip). For the older papers only Postscript files are provided.

You can also download a postscript version of both my Ph.D. thesis and my habilitation thesis.

Books
  1. Involution - The Formal Theory of Differential Equations and its Applications in Computer Algebra
    Springer-Verlag, Berlin/Heidelberg 2010, Algorithms and Computation in Mathematics, Vol. 24 (ISBN 3-642-01286-0)

Refereed Articles in Journals
  1. Anisotropic Solutions in the 5D Space-Time-Mass Theory (with Waldir L. Roque)
    General Relativity and Gravitation, 23 (1991) 1151-1168

  2. SUPERCALC - A REDUCE Package for Commutator Calculations
    Computer Physics Communications, 66 (1991) 363-376

  3. On the Arbitrariness of the General Solution of an Involutive Partial Differential Equation
    Journal of Mathematical Physics, 35 (1994) 486-498

  4. Pseudo Differential Operators and Integrable Systems in AXIOM
    Computer Physics Communications, 79 (1994) 329-340

  5. Arbitrariness of the General Solution and Symmetries
    Acta Applicandae Mathematicae, 41 (1995) 311-322

  6. On Moving Pseudo-Spherical Surfaces: A Generalized Weingarten System and its Formal Analysis (with Mark E. Johnston, Colin Rogers and Wolfgang K. Schief)
    Lie Groups and their Applications, 1 (1995) 124-136

  7. Involution and Constrained Dynamics I: The Dirac Approach (with Robin W. Tucker)
    Journal of Physics A - Mathematical and General, 28 (1995) 4431-4451

  8. Involution and Constrained Dynamics II: The Faddeev-Jackiw Approach
    Journal of Physics A - Mathematical and General, 28 (1995) 7315-7331

  9. Formal Analysis of the Cauchy Problem for a System Associated with the (2+1)-Dimensional Krichever-Novikov Equation (with Peter J. Vassiliou and Colin Rogers)
    Acta Applicandae Mathematicae, 42 (1996) 249-265

  10. Quantization of the Reduced Phase Space of Two-Dimensional Dilaton Gravity (with Robin W. Tucker)
    Physical Review D, 53 (1996) 4366-4373

  11. Involution and Symmetry Reductions
    Mathematical and Computer Modelling, 25 (1997) 63-73 (invited contribution)

  12. Position versus Momentum Projections for Constrained Hamiltonian Systems
    Numerical Algorithms, 19 (1998) 223-234

  13. Computer Algebra and Field Theories (with Jacques Calmet)
    Mathematics and Computer in Simulation, 45 (1998) 33-37

  14. Numerical Analysis of Constrained Hamiltonian Systems and the Formal Theory of Differential Equations
    Mathematics and Computer in Simulation, 45 (1998) 561-576

  15. Numerical Integration of Constrained Hamiltonian Systems Using Dirac Brackets
    Mathematics of Computation, 68 (1999) 661-681

  16. Involution and Constrained Dynamics III: Intrinsic Degrees of Freedom Count
    Technische Mechanik, 20 (2000) 137-146

  17. Completion to Involution and Semi-Discretisations
    Applied Numerical Mathematics, 42 (2002) 437-451

  18. An Efficient Algebraic Algorithm for the Geometric Completion to Involution (with Marcus Hausdorf)
    Applicable Algebra in Engineering, Communication and Computing, 13 (2002) 163-207

  19. Involutive Bases in the Weyl Algebra (with Marcus Hausdorf and Rainer Steinwandt)
    Journal of Symbolic Computation, 34 (2002) 181-198

  20. Taylor and Lyubeznik Resolutions via Gröbner Bases
    Journal of Symbolic Computation, 34 (2002) 597-608

  21. A Differential Equations Approach to Hamiltonian Systems (with Dirk Fesser and Dirk Saller)
    Reports on Mathematical Physics, 49 (2002) 345-359 (invited contribution)

  22. Differential Equations, Spencer Cohomology, and Computing Resolutions (with Larry A. Lambe)
    Georgian Mathematical Journal, 9 (2002) 723-772

  23. Involution Analysis of the Partial Differential Equations Characterising Hamiltonian Vector Fields
    Journal of Mathematical Physics, 44 (2003) 1173-1182

  24. Overdetermined Elliptic Systems (with Katsiaryna Krupchyk and Jukka Tuomela)
    Foundations of Computational Mathematics, 6 (2006) 309-351

  25. Existence and Construction of Vessiot Connections (with Dirk Fesser)
    Symmetry, Integrability, and Geometry: Methods and Applications (SIGMA), 5 (2009) 092

  26. A Combinatorial Approach to Involution and Delta-Regularity I: Involutive Bases in Polynomial Algebras of Solvable Type
    Applicable Algebra in Engineering, Communication and Computing, 20 (2009) 207-259

  27. A Combinatorial Approach to Involution and Delta-Regularity II: Structure Analysis of Polynomial Modules with Pommaret Bases
    Applicable Algebra in Engineering, Communication and Computing, 20 (2009) 261-338

  28. Unter- und Überbestimmte Systeme von Differentialgleichungen
    Mathematische Semesterberichte, 57 (2010) 231-268

  29. On the Inverse Syzygy Problem (with Eva Zerz and Marcus Hausdorf)
    Communications in Algebra, 38 (2010) 2037-2047

  30. Effective Genericity, Delta-Regularity and Strong Noether Position
    Communications in Algebra, 40 (2012) 3933-3949

  31. On the Free Resolution Induced by a Pommaret Basis (with Mario Albert, Matthias Fetzer and Eduardo Saenz-de-Cabezon)
    Journal of Symbolic Computation, 68/2 (2015) 4-26

  32. Detection of Hopf Bifurcations in Chemical Reaction Networks Using Convex Coordinates (with Hassan Errami, Markus Eiswirth, Dima Grigoriev, Thomas Sturm and Andreas Weber)
    Journal of Computational Physics, 291 (2015) 279--302

  33. Deterministic Genericity for Polynomial Ideals (with Amir Hashemi and Michael Schweinfurter)
    Journal of Symbolic Computation, accepted for publication

  34. A Pommaret Bases Approach to the Degree of a Polynomial Ideal (with Bentolhoda Binaei and Amir Hashemi)
    Applicable Algebra in Engineering, Communication and Computing, accepted for publication

Contributions in Proceedings or Collections, Unrefereed Articles
  1. BRST Quantization of String Theories - Applying REDUCE to High Energy Physics
    New Computing Techniques in Physics Research, D. Perret-Gallix, W. Wojcik (eds), Editions du CNRS, Paris 1990, pp. 595-600

  2. Formale Theorie partieller Differentialgleichungen
    Arbeitsgespräch Physik und Informatik - Informatik und Physik, D. Krönig, M. Lang (eds), Informatik-Fachberichte 306, Springer-Verlag, Berlin 1992, pp. 318-326

  3. Algorithmic Methods for Lie Pseudogroups (with Joachim Schü and Jacques Calmet)
    Proc. Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, N. Ibragimov, M. Torrisi, A. Valenti (eds), Kluwer, Dordrecht 1993, pp. 337-344

  4. Symbolische Behandlung von Differentialgleichungen (with Francois Ollivier, Fritz Schwarz, Felix Ulmer and Benno Fuchssteiner)
    Computeralgebra in Deutschland - Bestandsaufnahme, Möglichkeiten, Perspektiven. Fachgruppe Computeralgebra, Heidelberg, Passau 1993

  5. Using REDUCE for Replica Calculations (with Paul Lukowicz and Klaus R. Müller)
    Proc. Int. Conf. Artificial Neural Networks (ICANN '93), S. Gielen, B. Kappen (eds), Springer-Verlag, London 1993, pp. 716-721

  6. Computer Algebra and Differential Equations - An Overview
    mathPAD, 7 (1997) 34-49

  7. DETools: A Library for Differential Equations
    mathPAD, 9 (1999) 18-33

  8. Indices and Solvability for General Systems of Differential Equations
    Computer Algebra in Scientific Computing - CASC '99, V.G. Ghanza, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 1999, pp. 365-385 (invited contribution)

  9. Index Concepts for General Systems of Partial Differential Equations
    Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 81 (2001) 629-632 (Supplement, part 3) (Proc. Annual Meeting GAMM, Göttingen 2000)

  10. A Constructive Introduction to Involution (with Jacques Calmet and Marcus Hausdorf)
    Proc. Int. Symp. Applications of Computer Algebra - ISACA 2000, R. Akerkar (ed), Allied Publishers, New Delhi 2001, pp. 33-50 (invited contribution)

  11. Involution Analysis of Field Theories (with Jacques Calmet and Marcus Hausdorf)
    Proc. Encuentro de Algebra Computacional y Aplicaciones - EACA 2001, La Roja (Spain), J. Rubio (ed.), pp. 1-15 (invited contribution)

  12. Completion to Involution and Symmetry Analysis (with Marcus Hausdorf)
    Proc. Computer Algebra and Applications in Physics, Dubna 2001, V.P. Gerdt (ed.), pp. 169-179

  13. A MuPAD Library for Differential Equations (with Jay Belanger and Marcus Hausdorf)
    Computer Algebra in Scientific Computing - CASC 2001, V.G. Ghanza, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2001, pp. 25-42

  14. Perturbation versus Differentiation Indices (with Marcus Hausdorf)
    Computer Algebra in Scientific Computing - CASC 2001, V.G. Ghanza, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2001, pp. 323-337

  15. Perturbation versus Differentiation Indices (with Marcus Hausdorf)
    Proceedings in Applied Mathematics and Mechanics, 1 (2002) 514-515 (Proc. Annual Meeting GAMM, Zürich 2001)

  16. Involutive Bases in MuPAD I: Involutive Divisions (with Marcus Hausdorf)
    mathPAD, 11 (2002) 51-56 (invited contribution)

  17. On the Numerical Analysis of Overdetermined Linear Partial Differential Systems (with Marcus Hausdorf)
    Proc. Symbolic and Numerical Scientific Computation - SNSC '01, F. Winkler and U. Langer (eds), Lecture Notes in Computer Science 2630, Springer-Verlag, Berlin/Heidelberg 2003, pp. 152-167

  18. Structure Analysis of Polynomial Modules with Pommaret Bases
    Proceedings in Applied Mathematics and Mechanics, 2 (2003) 446-447 (Proc. Annual Meeting GAMM, Augsburg 2002)

  19. Overdetermined Elliptic Systems (with Jukka Tuomela)
    Proceedings in Applied Mathematics and Mechanics, 3 (2003) 485-486 (Proc. Annual Meeting GAMM, Abano Terme 2003)

  20. Deciding Ellipticity by Quantifier Elimination (with Andreas Weber)
    Computer Algebra in Scientific Computing - CASC 2003, V.G. Ghanza, E.W. Mayr, E.V. Vorozhtsov (eds.), TU München 2003, pp. 347-355

  21. Stable Underlying Equations for Constrained Hamiltonian Systems
    GAMM-Mitteilungen, 27 (2004) 25-45 (invited contribution)

  22. Vessiot Connections of Partial Differential Equations (with Dirk Fesser)
    Global Integrability of Field Theories - GIFT 2006, J. Calmet, W.M. Seiler, R.W. Tucker (eds.), Universitätsverlag Karlsruhe 2006, pp. 111-134

  23. Delta- and Quasi-Regularity for Polynomial Ideals (with Marcus Hausdorf and Mehdi Sahbi)
    Global Integrability of Field Theories - GIFT 2006, J. Calmet, W.M. Seiler, R.W. Tucker (eds.), Universitätsverlag Karlsruhe 2006, pp. 179-200

  24. Spencer Cohomology, Differential Equations, and Pommaret Bases
    Proc. Gröbner Bases and Symbolic Analysis, M. Rosenkranz, D.M. Wang (eds); de Gruyter, Berlin 2007, Radon Series on Computational and Applied Mathematics 2, pp. 169-216

  25. The Inverse Syzygy Problem in Algebraic Systems Theory (with Eva Zerz)
    Proceedings in Applied Mathematics and Mechanics, 10 (2010) 633-634 (Proc. Annual Meeting GAMM, Karlsruhe 2010)

  26. Parametric Qualitative Analysis of Ordinary Differential Equations: Computer Algebra Methods for Excluding Oscillations (with Andreas Weber, Thomas Sturm and Essam O. Abdel-Rahman)
    Computer Algebra in Scientific Computing - CASC 2010, V.P. Gerdt, W. Koepf, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2010, Lecture Notes in Computer Science 6244, pp. 267-279 (invited contribution)

  27. On Muldowney's Criteria for Polynomial Vector Fields with Constraints (with Hassan Errami, Thomas Sturm and Andreas Weber)
    Computer Algebra in Scientific Computing - CASC 2011, V.P. Gerdt, W. Koepf, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2011, Lecture Notes in Computer Science 6885, pp. 135-143

  28. Singularities in the Geometric Theory of Differential Equations (with Ulrike Kant)
    Dynamical Systems, Differential Equations and Applications (Proceedings 8th AIMS International Conference, Dresden 2010), W. Feng, Z. Feng, M. Graselli, A. Ibragimov, X. Lu, S. Siegmund, J. Voigt (eds.), AIMS 2012, Vol. 2, pp. 784-793

  29. Quasi-Stability versus Genericity (with Amir Hashemi and Michael Schweinfurter)
    Computer Algebra in Scientific Computing - CASC 2012, V.P. Gerdt, W. Koepf, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2012, Lecture Notes in Computer Science 7442, pp. 172-184

  30. Computing Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates (with Hassan Errami, Markus Eiswirth and Andreas Weber)
    Computer Algebra in Scientific Computing - CASC 2012, V.P. Gerdt, W. Koepf, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2012, Lecture Notes in Computer Science 7442, pp. 84-92

  31. Singularities of Implicit Differential Equations and Static Bifurcations
    Computer Algebra in Scientific Computing - CASC 2013, V.P. Gerdt, W. Koepf, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2013, Lecture Notes in Computer Science 8136, pp. 355-368

  32. Efficient Methods to Compute Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates (with Hassan Errami, Markus Eiswirth, Dima Grigoriev, Thomas Sturm and Andreas Weber)
    Computer Algebra in Scientific Computing - CASC 2013, V.P. Gerdt, W. Koepf, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2013, Lecture Notes in Computer Science 8136, pp. 88-99

  33. Deterministically Computing Reduction Numbers of Polynomial Ideals (with Amir Hashemi and Michael Schweinfurter)
    Computer Algebra in Scientific Computing - CASC 2014, V.P. Gerdt, W. Koepf, W.M. Seiler, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2014, Lecture Notes in Computer Science 8660, pp. 186-201

  34. Janet Bases and Resolutions in CoCoALib (with Mario Albert, Matthias Fetzer)
    Computer Algebra in Scientific Computing - CASC 2015, V.P. Gerdt, W. Koepf, W.M. Seiler, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2015, Lecture Notes in Computer Science 9301, pp. 15-29

  35. Algebraic Theory of Linear Systems: A Survey (with Eva Zerz)
    Surveys in Differential-Algebraic Equations II, A. Ilchmann, T. Reis (eds), Differential-Algebraic Equations Forum, Springer-Verlag, Berlin 2015, pp. 287-333

  36. Resolving Decompositions of Polynomial Modules (with Mario Albert)
    Computer Algebra in Scientific Computing - CASC 2016, V.P. Gerdt, W. Koepf, W.M. Seiler, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2016, Lecture Notes in Computer Science 9890, pp. 15-29

  37. SC-Square: Satisfiability Checking meets Symbolic Computation (with E. Abraham, J. Abbott, B. Becker, A. Bigatti, M. Brain, B. Buchberger, A. Cimatti, J.H. Davenport, M. England, P. Fontaine, S. Forrest, A. Griggio, D. Kroening und T. Sturm)
    Conference on Intelligent Computer Mathematics - CICM 2016, M. Kohlhase, M. Johansson, B. Miller, L. de Moura, F. Tompa (eds.), Lecture Notes in Artificial Intelligence 9791, pp. 28-43

  38. Improved Computation of Involutive Bases (with Bentolhoda Binaei and Amir Hashemi)
    Computer Algebra in Scientific Computing - CASC 2016, V.P. Gerdt, W. Koepf, W.M. Seiler, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2016, Lecture Notes in Computer Science 9890, pp 58-72

  39. Resolutions and Betti Numbers of Polynomial Modules via Involutive Bases (with Mario Albert and Matthias Fetzer)
    Proceedings in Applied Mathematics and Mechanics, 16 (2016) 3-6 (Proc. Annual Meeting GAMM, Braunschweig 2016)

  40. Dimension-Dependent Upper Bounds for Gröbner Bases (with Amir Hashemi)
    Proc. International Symposium on Symbolic and Algebraic Computation - ISSAC 2017, accepted for publication

Preprints and Technical Reports, Work in Progress
  1. Applying AXIOM to Partial Differential Equations
    Internal Report 95-17. Fakultät für Informatik, Universität Karlsruhe, 1995

  2. Generalized Tableaux and Formally Well-Posed Initial Value Problems
    Lancaster University Preprint 1995

  3. Computer Algebra and Differential Equations - An Overview
    Internal Report 97-25. Fakultät für Informatik, Universität Karlsruhe 1997

  4. Differential Equations in MuPAD I: An Object-Oriented Environment (with Marcus Hausdorf)
    Internal Report 2000-17. Fakultät für Informatik, Universität Karlsruhe 2000

  5. Involutive Bases in MuPAD II: Polynomial Algebras of Solvable Type (with Marcus Hausdorf)
    Preprint Universität Heidelberg 2003

  6. Marked Bases Over Quasi-Stable Modules (with Mario Albert, Cristina Bertone and Margherita Roggero)
    Preprint Unis Kassel/Torino 2015, arXiv:1511.03547

  7. Singular Initial Value Problems for Quasi-Linear Ordinary Differential Equations (with Matthias Seiß)
    In preparation

  8. Involution Analysis of Field Theories (with Vladimir P. Gerdt and Arsen Khvedelidze)
    In preparation

  9. Impetus-Striction Formalism and the Numerical Integration of Constrained Hamiltonian Systems
    In preparation

Editorial Activities
  1. Computational Geometry for Differential Equations
    Applicable Algebra in Engineering, Communication and Computing, 11(5) (2001)

  2. Under- and Overdetermined Systems of Algebraic or Differential Equations (with J. Calmet and M. Hausdorf)
    Fakultät für Informatik, Universität Karlsruhe 2002

  3. Global Integrability of Field Theories (with J. Calmet and R.W. Tucker)
    Universitätsverlag Karlsruhe 2006, ISBN 3-86644-035-9

  4. Applicable Algebra and Artificial Intelligence (with J. Rubio)
    Annals of Mathematics and Artificial Intelligence, 56(3/4) 2009

  5. Computer Algebra in Scientific Computing, Warsaw 2014 (with V.P. Gerdt, W. Koepf, E.V. Vorozhtsov)
    Springer-Verlag 2014, ISBN 978-3-319-10514-7

  6. Computer Algebra in Scientific Computing, Aachen 2015 (with V.P. Gerdt, W. Koepf, E.V. Vorozhtsov)
    Springer-Verlag 2015, ISBN 978-3-319-24020-6

  7. Computer Algebra in Scientific Computing, Bucharest 2016 (with V.P. Gerdt, W. Koepf, E.V. Vorozhtsov)
    Springer-Verlag 2016, ISBN 978-3-319-45640-9

  8. Proceedings Applications of Computer Algebra (Kassel 2016) (with N. Dana-Picard, W. Koepf,I. Kotsireas, Z. Kovacs, A. Prokopenya)
    Mathematics in Computer Science, 11(3-4) (2017)

  9. Computer Algebra in Scientific Computing, Beijing 2017 (with V.P. Gerdt, W. Koepf, E.V. Vorozhtsov)
    Springer-Verlag 2017, ISBN 978-3-319-45640-9

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