Computer differential and difference algebra and its applications

Special Session at the 23rd Conference on Applications of Computer Algebra,

  Jerusalem, July 17-21, 2017


Algebraic differential and difference 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 (respectively, difference) computer algebra studies algebraic differential (respectively, difference) equations in a constructive way that extends the methods and algorithms of commutative algebra and algebraic geometry.
Even though many computational methods in difference algebra have been developed as difference counterparts of the corresponding techniques for differential algebraic structures, the computational difference algebra is a rapidly developed theory with its own methods that are very useful in the study of systems of equations in finite differences, functional equations, differential equations with delay, algebraic structures with operators, theory of discrete-time nonlinear systems and many other areas.
The main goal of the session is to look at the computational problems in differential (respectively, difference) algebra to explore new constructive ideas and approaches oriented toward various applications.


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

  • Linear Differential and Difference Equations and Systems
  • Differential and Difference Gröbner (Standard) Bases
  • Differential and Difference Characteristic Sets
  • Triangular Decomposition of Algebraic Differential and Difference Equations and Systems
  • Lie Symmetry Analysis of Differential and Difference Equations
  • Algorithmic Generation of Finite Difference Approximations to PDEs
  • Consistency and Stability Analysis of Finite Difference Approximations
  • Difference-Differential Polynomials and Systems
  • Differential and Difference Dimension Polynomials
  • Software Packages oriented toward Construction of Differential and Difference Gröbner (Standard) Bases and Characteristic Sets
  • Recurrence Relations for Feynman Integrals and their Reduction

If you are interested in giving a presentation at this session, please email an abstract to one of the organizers. The duration of a talk is to be 30 minutes including time for discussion.
Submission of talks : see important dates.
The submissions are requested a specific format for the abstracts: 1-2 pages, with some references. This can help the readers to understand what it is exactly about and also yield some homogeneity to the abstract book.

More information about the conference can be found at the ACA 2017 conference web page .




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