Computational Differential and Difference Algebra and its Applications

Special Session at the 25th Conference on Applications of Computer Algebra (ACA- 2019),

  Montréal, Canada, July 16-20, 2019


Algebraic differential and difference equations and systems of such equations arise in many areas of mathematics, natural sciences and engineering. One can say that difference equations relate to differential equations as discrete mathematics relates to continuous mathematics. Differential and difference computer algebra concerns the study of systems of differential and difference equations in a constructive way that extends methods and algorithms of commutative algebra and algebraic geometry. The main goal of the session is to consider actual computational problems in differential and difference algebra to explore ew constructive ideas and approaches oriented toward various applications.


Topics of the session include, but are not limited to:

  • Systems of Differential, Difference and Difference-Differential Algebraic Equations
  • Differential and Difference Gröbner (Standard) and Involutive Bases
  • Differential and Difference Characteristic Sets
  • Triangular Decompositions of Differential and Difference Systems
  • Differential and Difference Elimination
  • Algorithmic Generation of Finite Difference Approximations to PDEs
  • Consistency and Stability Analysis of Finite Difference Approximations
  • Differential, Difference and Difference-Differential Polynomials
  • Software Packages for Differential and Difference Algebra
  • Applications of Differential and Difference Algebra in Mathematics and Natural Sciences

If you are interested in giving a presentation at this session, please email an abstract to one of the organizers (including  both the  LaTeX source and a compiled PDF version).  We suggest that abstracts will be 1-2 pages, with some references.

Detailed information about the session, LaTex template for abstracts and deadline is posted at the ACA2019 conference web page

Template tex source files : [] (Please compile the abstract with ACA2019_abstract_pdfgen.tex).


Differential transcendence of elliptic hypergeometric functions through Galois theory
Carlos E. Arreche (The University of Texas at Dallas, Richardson, TX, USA),
Thomas Dreyfus (Institut de Recherche Mathématique Avancée, Strasbourg, France),
Julien Roques (Institut Camille Jordan, Université de Lyon 1, Lyon, France)

The generalized Weyl Poisson algebras and their Poisson simplicity criterion
V. V. Bavula (University of Sheffield, Sheffield, UK)

Algebraic invariants and Qualitative theory of differential equations
Dahira Dali (Université des Sciences et de la Technologie Houari Boumediene, Algiers, Algeria)

A computational method for the strong minimality of differential equations
James Freitag (University of Illinois at Chicago, Chicago, IL, USA)

Order bounds for differential elimination algorithms
Richard Gustavson (Manhattan College, Riverdale, New York, USA)

Hilbert-type Functions of Non-reflexive Prime Difference Polynomial Ideals
Alexander Levin (The Catholic University of America, Washington, D.C., USA)

A Maple package for solving algebraic differential equations by algebro-geometric methods
Johann J. Mitteramskogler, Wolfgang Schreiner and Franz Winkler
(Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Linz, Austria)

A differential algebra approach to parameter identifiability in ODE models
Alexey Ovchinnikov (Queens College and CUNY Graduate Center, New York, NY, USA),
Gleb Pogudin (Courant Institute, New York University, New York, NY, USA),
Peter Thompson (CUNY Graduate Center, New York, NY, USA)

On the Complexity of Computing the Galois Group of a Linear Differential Equation
Mengxiao Sun (The Graduate Center, CUNY, New York, NY, USA)

HNN-extension of free Rota-Baxter Lie algebras
Chia Zargeh (Departamento de Matemática, UFBA, Salvador, BA, Brazil)



Last modified:   May 19, 2019   by Alla Bogolubskaya