SUPERCALC - A REDUCE Package for Commutator Calculations
Computer Physics Communications, 66 (1991) 363-376
Anisotropic Solutions in the 5D Space-Time-Mass Theory (with Waldir L. Roque)
General Relativity and Gravitation, 23 (1991) 1151-1168
Pseudo Differential Operators and Integrable Systems in AXIOM
Computer Physics Communications, 79 (1994) 329-340
On the Arbitrariness of the General Solution of an Involutive
Partial Differential Equation
Journal of Mathematical Physics, 35 (1994) 486-498
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
Arbitrariness of the General Solution and Symmetries
Acta Applicandae Mathematicae, 41 (1995) 311-322
Involution and Constrained Dynamics I: The Dirac Approach (with Robin W. Tucker)
Journal of Physics A - Mathematical and General, 28 (1995) 4431-4451
Involution and Constrained Dynamics II: The Faddeev-Jackiw Approach
Journal of Physics A - Mathematical and General, 28 (1995) 7315-7331
Quantization of the Reduced Phase Space of Two-Dimensional
Dilaton Gravity (with Robin W. Tucker)
Physical Review D, 53 (1996) 4366-4373
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
Involution and Symmetry Reductions
Mathematical and Computer Modelling, 25 (1997) 63-73 (invited contribution)
Computer Algebra and Field Theories (with Jacques Calmet)
Mathematics and Computer in Simulation, 45 (1998) 33-37
Numerical Analysis of Constrained Hamiltonian Systems and the Formal
Theory of Differential Equations
Mathematics and Computer in Simulation, 45 (1998) 561-576
Position versus Momentum Projections for Constrained Hamiltonian
Systems
Numerical Algorithms, 19 (1998) 223-234
Numerical Integration of Constrained Hamiltonian Systems
Using Dirac Brackets
Mathematics of Computation, 68 (1999) 661-681
Involution and Constrained Dynamics III: Intrinsic Degrees of Freedom
Count
Technische Mechanik, 20 (2000) 137-146
Completion to Involution and Semi-Discretisations
Applied Numerical Mathematics, 42 (2002) 437-451
Involutive Bases in the Weyl Algebra (with Marcus Hausdorf and Rainer Steinwandt)
Journal of Symbolic Computation, 34 (2002) 181-198
A Differential Equations Approach to Hamiltonian Systems (with Dirk Fesser and Dirk Saller)
Reports on Mathematical Physics, 49 (2002) 345-359 (invited contribution)
Taylor and Lyubeznik Resolutions via Gröbner Bases
Journal of Symbolic Computation, 34 (2002) 597-608
An Efficient Algebraic Algorithm for the Geometric
Completion to Involution (with Marcus Hausdorf)
Applicable Algebra in Engineering, Communication and
Computing, 13 (2002) 163-207
Differential Equations, Spencer Cohomology, and Computing Resolutions (with Larry A. Lambe)
Georgian Mathematical Journal, 9 (2002) 723-772
Involution Analysis of the Partial Differential Equations
Characterising Hamiltonian Vector Fields
Journal of Mathematical Physics, 44 (2003) 1173-1182
Overdetermined Elliptic Systems (with Katsiaryna Krupchyk and Jukka Tuomela)
Foundations of Computational Mathematics, 6 (2006) 309-351
Existence and Construction of Vessiot Connections (with Dirk Fesser)
Symmetry, Integrability, and Geometry: Methods and
Applications (SIGMA), 5 (2009) 092
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
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
On the Inverse Syzygy Problem (with Eva Zerz and Marcus Hausdorf)
Communications in Algebra, 38 (2010) 2037-2047
Unter- und Überbestimmte Systeme von Differentialgleichungen
Mathematische Semesterberichte, 57 (2010) 231-268
Effective Genericity, Delta-Regularity and Strong Noether Position
Communications in Algebra, 40 (2012) 3933-3949
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
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
Satisfiability Checking and 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 and T. Sturm)
ACM Communications in Computer Algebra, 50 (2016) 145-147
Deterministic Genericity for Polynomial Ideals (with Amir Hashemi and Michael Schweinfurter)
Journal of Symbolic Computation, 86 (2018) 20-50
Resolving Decompositions for Polynomial Modules (with Mario Albert)
Mathematics, 6 (2018) 161 (invited contribution)
A Pommaret Bases Approach to the Degree of a Polynomial Ideal (with Bentolhoda Binaei and Amir Hashemi)
Applicable Algebra in Engineering, Communication and
Computing, 29 (2018) 283-301
The SYMBIONT Project: Symbolic Methods for Biological Networks (with F. Boulier, F. Fages, O. Radulescu, S.S. Samal, A. Schuppert, T. Sturm, S. Walcher and A. Weber)
ACM Communications in Computer Algebra, 52 (2019) 67-70
Noether Bases and Their Applications (with Amir Hashemi and Hossein Parnian)
Bulletin of the Iranian Mathematical Society, 45 (2019) 1283-1301
Dimension and Depth Dependent Upper Bounds in Polynomial Ideal Theory (with Amir Hashemi)
Journal of Symbolic Computation, 98 (2020) 47-64
Computing Quot Schemes via Marked Bases Over Quasi-Stable Modules (with Mario Albert, Cristina Bertone and Margherita Roggero)
Journal of Algebra, 550 (2020) 432-470
On the Numerical Analysis and Visualisation of Implicit
Ordinary Differential Equations (with Elishan Braun and Matthias Seiß)
Mathematics in Computer Science, 14 (2020) 281-293
Computing the Resolution Regularity of Bi-Homogeneous Ideals (with Nasibeh Aramideh and Amir Hashemi)
Journal of Symbolic Computation, 103 (2021) 141-156
Singular Initial Value Problems for Quasi-Linear Ordinary
Differential Equations (with Matthias Seiß)
Journal of Differential Equations, 281 (2021) 258-288
Singularities of Algebraic Differential Equations (with Markus Lange-Hegermann and Daniel Robertz and Matthias Seiß)
Advances in Applied Mathematics, 131 (2021) 102266
Degree Upper Bounds for Involutive Bases (with Amir Hashemi and Hossein Parnian)
Mathematics in Computer Science, 15 (2021) 233-254
A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations (with Matthias Seiß and Thomas Sturm)
Mathematics in Computer Science, 15 (2021) 333-352
An Involutive GVW Algorithm and the Computation of Pommaret Bases (with Amir Hashemi, Thomas Izgin and Daniel Robertz)
Mathematics in Computer Science, 15 (2021) 419-452
Relative Gröbner and Involutive Bases For Ideals In Quotient Rings (with Amir Hashemi and Matthias Orth)
Mathematics in Computer Science, 15 (2021) 453-482
Is the Diatom Sex Clock a Clock? (with Thomas Fuhrmann-Lieker, Roland Klassen, Nico Kubetschek and Jonas Ziebarth)
Journal of the Royal Society Interface, 18 (2021) 20210146
No Chaos in Dixon's system (with Matthias Seiß)
International Journal of Bifurcation and Chaos, 31 (2021) 2150044
Computation of Macaulay Constants and Degree Bounds
for Gröbner Bases (with Amir Hashemi and Hossein Parnian)
Journal of Symbolic Computation, 111 (2022) 44-60
Complementary Decompositions of Monomial Ideals and Involutive Bases (with Amir Hashemi and Matthias Orth)
Applicable Algebra in Engineering, Communication and
Computing, 33 (2022) 791--821
Recursive Structures in Involutive Bases Theory (with Amir Hashemi and Matthias Orth)
Journal of Symbolic Computation, 118 (2023) 32-68
On the Numerical Integration of Singular Initial and Boundary Value
Problems for Generalised Lane-Emden and Thomas-Fermi Equations (with Matthias Seiß)
Applied Mathematics and Computation, 466 (2024) 128446
A Single Exponential Time Algorithm for Regular Sequence Test (with Amir Hashemi and Benyamin M.-Alizadeh and Hossein Parnian)
Journal of Algebra and its Applications, 23 (2024) 2450145 (20 pages)
Open Covers and Lex Points of Hilbert Schemes over Quotient Rings via Relative Marked Bases (with Cristina Bertone and Francesca Cioffi and Matthias Orth)
Experimental Mathematics, accepted for publication
Machine Learning Parameter Systems, Noether
Normalisations and Quasi-stable Positions (with Amir Hashemi and Mahshid Mirhashemi)
Journal of Symbolic Computation, 126 (2025) 102345
|
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
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
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
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
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
Computer Algebra and Differential Equations - An Overview
mathPAD, 7 (1997) 34-49
DETools: A Library for Differential Equations
mathPAD, 9 (1999) 18-33
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)
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)
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)
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)
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
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
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
Perturbation versus Differentiation Indices (with Marcus Hausdorf)
Proceedings in Applied Mathematics and Mechanics, 1 (2002) 514-515 (Proc. Annual Meeting GAMM, Zürich 2001)
Involutive Bases in MuPAD I: Involutive Divisions (with Marcus Hausdorf)
mathPAD, 11 (2002) 51-56 (invited contribution)
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
Structure Analysis of Polynomial Modules with Pommaret Bases
Proceedings in Applied Mathematics and Mechanics, 2 (2003) 446-447 (Proc. Annual Meeting GAMM, Augsburg 2002)
Overdetermined Elliptic Systems (with Jukka Tuomela)
Proceedings in Applied Mathematics and Mechanics, 3 (2003) 485-486 (Proc. Annual Meeting GAMM, Abano Terme 2003)
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
Stable Underlying Equations for Constrained Hamiltonian Systems
GAMM-Mitteilungen, 27 (2004) 25-45 (invited contribution)
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
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
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
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)
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)
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
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
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
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
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
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
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
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
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 (invited contribution)
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
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
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
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)
SC^2 Challenges: When Satisfiability Checking and
Symbolic Computation Join Forces (with E. Abraham, J. Abbott, B. Becker, A. Bigatti, M. Brain,
A. Cimatti, J.H. Davenport, M. England, P. Fontaine,
S. Forrest, V. Ganesh, A. Griggio and D. Kroening)
Proceedings Automated Reasoning: Challenges, Applications,
Directions, Exemplary Achievements (ARCADE 2017), G. Reger, D. Traytel
(eds.), EPiC Series in Computing
51, pp. 6-10
Dimension-Dependent Upper Bounds for Gröbner Bases (with Amir Hashemi)
Proc. International Symposium on Symbolic and Algebraic
Computation - ISSAC 2017, M. Burr (ed.), ACM, New York 2017, pp. 189--196
Computation of Pommaret Bases Using Syzygies (with Bentolhoda Binaei and Amir Hashemi)
Computer Algebra in Scientific Computing - CASC 2018,
V.P. Gerdt, W. Koepf, W.M. Seiler, E.V. Vorozhtsov (eds.), Springer-Verlag,
Berlin 2018, Lecture Notes in Computer Science 11077, pp. 51-66
Algebraic and Geometric Analysis of Singularities of Implicit
Differential Equations (with Matthias Seiß)
Computer Algebra in Scientific Computing - CASC 2020,
F. Boulier, M. England, T. Sadykov, E.V. Vorozhtsov (eds.), Springer-Verlag,
Cham 2020, Lecture Notes in Computer Science 12291, pp. 14-41 (invited contribution)
Size-Resolved Modeling of Diatom Populations:
Old Findings and New Insights (with Jonas Ziebarth and Thomas Fuhrmann-Lieker)
The Mathematical Biology of Diatoms, J.L. Pappas (ed.),
Wiley-Scrivener, Beverly 2023, pp.~19-61
|