Computational Differential and Difference Algebra and its Applications

Computational Differential and Difference Algebra and Their Applications
Special Session at the 30th International Conference on
Applications of Computer Algebra (July 14-18, 2025, Crete, Greece)

Organizers:

Roberto La Scala (University of Bari Aldo Moro, Bari, Italy)

Alexander Levin (The Catholic University of America, Washington, D.C., USA)

Daniel Robertz (RWTH Aachen University, Aachen, Germany)

Schedule:

TBD

Talks:

Vladimir Bavula, Affirmative answer to the Question of Leroy and Matczuk on injectivity of endomorphisms of semiprime left Noetherian rings with large images

Thierry Combot, Symbolic integration on a planar differential foliation

Bo Huang, Ivan Mastev, Valery Romanovski, Integrability and Linearizability of a Family of Three-Dimensional Polynomial Systems

Roberto La Scala, Stream cipher over Finite Fields: A Difference Algebra Approach

Alexander Levin, Joseph Baranoski, Gröbner type Bases with Respect to the Effective Order and Bivariate Dimension Polynomials of Difference Modules

V. Ravi Srinivasan, Partha Kumbhakar, Iterated strongly normal extensions and nonlinear differential equations

Raffaele Vitolo, A Reduce package for Differential Operators in Mathematical Physics and Theoretical Physics

Jiaqi Meng, Jing Yang, Subresultants of Several Ore Polynomials

Objectives:

Algebraic differential and difference equations and systems of such equations arise in many areas of mathematics and in a wide range of subject areas including physics, biology, chemistry, economics, and engineering. 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 discuss recent developments in computational methods of differential and difference algebra, as well as to explore new ideas and approaches oriented toward various applications of these methods.

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
Dimension Characteristics of Differential and Difference Algebraic Structures
Difference Equations over Finite Fields and Their Applications
Software Packages for Differential and Difference Algebra
Applications of Differential and Difference Algebra in the Sciences

Submissions:

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) by 31 May 2025. We suggest that abstracts will be 1-2 pages, with some references. Detailed information about the conference and a LaTeX template for abstracts will be posted at the ACA 2025 web page .

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