JuliaCon 2026

Julia has become a highly valuable asset for both pure‑mathematics research and applied‑science workflows that rely on exact or certified computations.
Recent advances in packages such as AbstractAlgebra.jl, AlgebraicSolving.jl, DynamicPolynomials.jl, Groebner.jl, HomotopyContinuation.jl, OSCAR.jl, and Symbolics.jl, and their integration into higher‑level ecosystems (e.g. ModelingToolkit.jl, Catalyst.jl) illustrate how Julia bridges algorithmic theory with real‑world applications.

Computer Algebra: A Broad Perspective

Traditionally, computer algebra tools aim to produce exact results, not approximations.
Efficient algorithms and implementations, for example for linear algebra over finite fields, integers, rationals, and other exact domains, remain central to the field.
At the same time, a growing class of algorithms relies on inexact computations (e.g., floating-point arithmetic, SIMD, or GPUs) while still producing exact or certified results.
Examples include the LLL algorithm or polynomial factorization.
In addition, techniques such as interval arithmetic and certified numerics are becoming increasingly common.
Beyond their role in exact computation, numerical and symbolic–numeric methods are also of intrinsic interest in applications such as machine learning, chemistry, robotics, and other applied sciences.
In this minisymposium, we adopt a broad view of computer algebra that encompasses all of these perspectives.

Why Julia for Computer Algebra?

Julia offers several compelling advantages for research and development in computer algebra:

• By addressing the two-language problem, Julia enables both developers and users to write high-level code while still producing high-performance implementations with access to low-level functionality when needed.
• Julia supports rapid prototyping and interactive experimentation with algorithmic ideas via the REPL and notebook-based workflows.
• The combination of multiple dispatch, generic programming, and parametric types is particularly well suited for working with algebraic structures.
• Excellent support for foreign-function interfaces (e.g. via ccall or packages such as CxxWrap or PythonCall) facilitates integration with existing, highly optimized tools and libraries such as FLINT, GAP, GMP, Polymake, or Singular.

These strengths have led to increasing adoption of Julia-based computer algebra tools. For example, the OSCAR.jl system is built around the Julia ecosystem and is already used in research publications, while HomotopyContinuation.jl is widely used in applied algebraic geometry. Julia is also increasingly used for teaching abstract algebra, linear algebra over rings, and computational number theory. Bringing together computer algebra researchers and the broader Julia community therefore offers a unique opportunity for interdisciplinary collaboration and knowledge transfer.

Aims of the Minisymposium

The minisymposium will showcase both the development of core computer-algebra tools and the ways these tools are applied in modern scientific and engineering problems. By highlighting end-to-end reproducible workflows, we aim to lower the entry barrier for researchers, educators, and developers, and to foster collaboration across communities that are often separated in practice, including algorithm designers, package maintainers, and domain scientists. Consequently, the aims of the minisymposium include:

• introducing computer algebra tools to new audiences within the Julia community;
• demonstrating accessible Julia-based workflows that lower barriers to entry for both Julia users and domain experts;
• encouraging cross-disciplinary collaboration and open-source contributions that broaden Julia’s impact in algebra research.

Scientific Scope

In terms of scope, the minisymposium spans both theoretical and applied aspects of computer algebra.
On the theoretical side, we welcome contributions in algebra, algebraic and polyhedral geometry, and number theory, ranging from foundational topics such as groups, rings, and vector spaces to more advanced areas including schemes, class field theory, and representation theory.
On the applied side, we invite work involving computer algebra methods in fields such as cryptography, coding theory, control theory, machine learning, robotics, physics (e.g. Feynman integrals), or chemistry (e.g. crystallographic groups).
We also welcome contributions related to interactions with formalized mathematics and proof assistants (such as Lean or Rocq), for example in the context of verified computations or the generation of formal certificates.

Submissions and Contributions

We invite submissions from developers and users of computer algebra software, and anyone in between, including talks that highlight software projects and their impact on user empowerment.
Contributions by developer–user pairs are especially welcome.
The minisymposium is open to abstracts from all areas in and adjacent to computer algebra, including, but not limited to, the following examples:

• implementations of algebraic algorithms in Julia;
• applications of Julia-based computer algebra tools in the natural sciences and engineering;
• research conducted using Julia computer algebra packages;
• interfaces to non-Julia computer algebra systems and libraries, and cross-package integration;
• symbolic–numeric workflows: representing and manipulating algebraic problems in Julia, integration with solvers, and downstream analysis;
• databases of algebraic objects created with or made available in Julia;
• visualization of algebraic structures and objects;
• benchmarking, reproducibility, and FAIR research principles.

We hope that this minisymposium will bring together researchers and developers who do not typically interact, and we warmly encourage submissions from a broad range of communities and perspectives.