Difference computer algebra and its applications

Special Session at the 22nd Conference on Applications of Computer Algebra,

 August 1st - 4th, 2016. Kassel University, Germany


Algebraic 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. Difference computer algebra studies algebraic 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 system 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 algebra to explore new constructive ideas and approaches to computational difference algebra oriented on various applications.


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

  • Linear Difference Equations and Systems
  • Difference Gröbner (Standard) Bases
  • Difference Characteristic Sets
  • Algorithmic Generation of Finite Difference Approximations to PDEs
  • Consistency and Stability Analysis of Finite Difference Approximations
  • Difference-Differential Polynomials and Systems
  • Software Packages for Construction of 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. Tentative abstract submission deadline is May 25, 2016.

More information about the session can be found at the ACA2016 conference web page




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