OSCAR Newsletter – August 2026

Hello, OSCAR Community!

Welcome to the August edition of the OSCAR newsletter! We are excited to share the latest updates, features, and achievements from our community.

Version 1.8.0 Released!

New features as compared to version 1.7.2 include:

• Algebraic Geometry: Introduced DrawingCurves, a new experimental project for drawing real plane curves. Added algorithm option for ideal_membership of FreeAssociativeAlgebraIdeal. Fixed a rare Groebner basis error in quantum_symmetric_group.
• Number Theory: Added new invariant function based on graph hash for integer lattices. Extended the use of databases of ZZLat in QuadFormAndIsom. Fixed a bug for odd lattices in automorphism group and isometry computations of quadratic lattices and tuned the heuristics.
• Combinatorics: Added tutte_group, is_tutte_realizable, bergman_fan for matroids and on_graph for acting on a graph with a PermGroupElem. Fixed a bug and achieved a speedup in tutte_group. Added equality and hash for Graph and GraphMap, isomorphism functionality for edge-labeled graphs, and methods checking for transversals in matroids.
• Polyhedral Geometry: Added contains and contains_in_interior for polyhedra and cones, as well as common_refinement also for polyhedral fans. Migrated slack ideals from polymake to OSCAR. Added n_rays_modulo_lineality and n_minimal_faces.
• Commutative Algebra: Now allowing general subquotient modules as input to vector_space_dimension. Added linear solving for matrices over multivariate polynomial and Laurent rings. Introduced cohomology rings of complexes with a DG-algebra structure. Achieved a speedup of vector_space_basis for SubquoModule. Refactored existing code for ungraded modules over a MPolyLocRing localized at a point and extended its functionality to modules with true sub-part. Improved performance for vector_space_dim and vector_space_basis by using M.quo and its cached groebner_basis. Added support for sparse matrices for transformations in Groebner basis computations, and a modular algorithm for determinants of matrices over univariate polynomial rings over the integers.
• Groups: Added maximal_supersolvable_quotient, character_table_rational, and regular_action_homomorphism for finite groups. Now allowing matrix_group(::Ring, ::Vector). Optimized stabilizer(G, v, permuted).
• Miscellaneous: Added kostant_kumar_character and dual for roots and coroots in Lie theory. Added is_feasible(::TropicalPolyhedron) and visualize(::TropicalPolyhedron) in tropical geometry. Updated AbstractAlgebra to v0.50, GAP.jl to v0.17 and Nemo to v0.56. Changes related to serializing data in the MRDI file format.
• For more details on the newest release, visit the GitHub Release or our website.

Papers and Projects Using OSCAR:

• Ryan Batubara, Jack J Garzella, Yongyuan Huang, and Maximus Mellberg describe in their new preprint Newton strata realization for hypersurfaces via explicit p-adic cohomology some of the algorithms used in the DeRham.jl package and its dependencies. This package currently implements point-counting algorithms for projective hypersurfaces in Julia. Its design allows usage within the OSCAR ecosystem, especially Nemo.jl. It also supports GPU hardware for counting points via CUDA.jl. Furthermore, the paper describes some new examples of varieties that the authors found using these algorithms.
• Until last Thursday, complete lists of isomorphism types of finite groups were known only for groups with at most 14 conjugacy classes, as documented, for example, in OEIS and the OSCAR documentation. Thomas Breuer has now pushed this bound to 16 by writing code that inductively constructs representatives of isomorphism classes of groups with few conjugacy classes. After first verifying the previously known results, he computed that there are 73 isomorphism types of groups with 15 conjugacy classes and 131 isomorphism types with 16 conjugacy classes. The largest group with at most 16 conjugacy classes is the Mathieu group M₂₂, of order 443,520 and with 12 conjugacy classes. Thomas Breuer is excited to see how far this strategy will take him. The list of groups with 17 conjugacy classes will include the Mathieu group M₂₃, of order 10,200,960. Hopefully, there will be another announcement in the next newsletter!

Upcoming Events:

• JuliaCon 2026 - Mainz, Germany · Aug 10-15, 2026
  • Featuring the minisymposium: Symbolic and Numerical Methods in (Nonlinear) Algebra.
• albatross-2026: ALgeBrAic meThods foR pOlynomial System Solving 2026 - Paris, France · Sep 01-04, 2026
• DMV Annual Meeting 2026 - Konstanz, Germany · Sep 07-10, 2026
• TRR 195 - Annual Meeting - Aachen, Germany · Sep 21-24, 2026
• OSCAR Developer Meeting - Berlin, Germany · Jul 12-13, 2027
• OSCAR Summer School - Berlin, Germany · Jul 14-16, 2027

Developer Spotlight:

Janika Peters (Total contributions to OSCAR last 12 months: 13 commits; 2,500 added lines of code)

Janika Peters is a master's student at RWTH Aachen University and a student assistant for OSCAR. She works on monomial bases of Demazure modules of Lie algebras, and in her bachelor's thesis she implemented basic functionality for linear algebraic groups. Follow her on GitHub under the username janikapeters.

OSCAR in the movies!

Should OSCAR be awarded an Oscar? You can decide, since we started rolling out the first few OSCAR movies! You can check them out on tube.mathe. Meet some of the OSCAR developers in personal interviews, and let our mascot sloth OSCAR teach you about Galois theory and Ehrhart polynomials.

These videos and other content will also be slowly rolled out on our newly created YouTube and Instagram channels.

Try OSCAR online!

If you're curious about trying OSCAR, but don't want to install anything yet, you can now try OSCAR online. It works completely within your browser, using Jupyter notebooks hosted by the NFDI JupyterHub service.

OSCAR-Shop:

Visit the OSCAR-Shop for exclusive merchandise and show your support for the project in style.

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Get Involved:

Do you want to contribute to the project? Find more information at our Contributor Guide to learn how to help-from code and documentation to outreach and community support.

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Best regards,
The OSCAR Team