OSCAR Newsletter – November 2026

Hello, OSCAR Community!

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

Version 1.8.2 Released!

New features as compared to version 1.8.0 include:

Toric Geometry: Fixed degree of rank-one toric line bundles.
Combinatorics: Fixed is_isomorphic for matroids.
Lie Theory: Fixed dual(::RootSpaceElem) for a zero input.
Commutative Algebra: Sped up arithmetic in simplicial cohomology rings (only affects experimental parts of OSCAR).
Miscellaneous: Overhauled linear algebra documentation.
For more details on the newest release, visit the GitHub Release or our website.

Papers and Projects Using OSCAR:

Annalisa Grossi and Stevell Muller, in their Corrigendum to "Nonsymplectic automorphisms of prime order on O'Grady's sixfolds", correct the lattice theoretic classification in a previous paper of Grossi's, by including some missing cases and explaining how to recover them. They used OSCAR to compute and correct their original tables listing, among others, invariant and coinvariant sublattices of effective nonsymplectic groups G ⊂ O(L) on manifolds of O'Grady's 6-dimensional deformation type.
Jie Fu, in his preprint Remarks on Lattice Actions Corresponding to Automorphism Groups of Smooth Cubic Fourfolds, completes the calculation of group actions on the primitive integral cohomology lattice for all of the 156 families in the previously known classification. He distinguishes similar families, determines the remaining action-maximal cases, and uses restriction to complete the list. The generic algebraic lattices for each family are also determined. The calculations mainly depend on OSCAR.
Simon Brandhorst and Tommy Hofmann, in their preprint Automorphisms and canonical forms of integer lattices, improve the Piesken–Souvignier algorithm for computing automorphism groups and isometries of positive definite integer quadratic lattices by exploiting characteristic sublattices and refining vector enumeration. For lattices with roots, they also use the Weyl group to accelerate the computation of canonical forms. In experiments with concrete implementations in OSCAR, they demonstrate substantial speedups and show that canonical forms can be computed at a cost comparable to that of computing automorphism groups.
Anne Frühbis-Krüger, Michael Joswig, and Lars Kastner, in their preprint A Known M-Curve of Degree 8 in OSCAR, show how OSCAR can be used to retrace geometric constructions of plane algebraic curves and provide topologically correct and visually pleasing drawings. They illustrate their approach on Shustin's construction from 1987 of a particular M-curve of degree eight. They arrive at an explicit homogeneous trivariate polynomial with rational coefficients, and provide a computational proof of all claimed properties of Shustin's original article. They also provide further examples on drawing curves with OSCAR in their GitHub repository.

Upcoming Events:

Women in Algebra and Symbolic Computation IV - Bad Dürkheim, Germany · Dec 07-09, 2026
40 Years of GAP - Aachen, Germany · Dec 10-11, 2026
LuCaNT 2027 - Luminy, France · Jun 21-25, 2027
OSCAR Developer Meeting - Berlin, Germany · Jul 12-13, 2027
OSCAR Summer School - Berlin, Germany · Jul 14-16, 2027

Developer Spotlight:

Matthias Zach (Total contributions to OSCAR last 12 months: 45 commits; 5,974 added lines of code)

Matthias Zach is a postdoctoral researcher at RPTU Kaiserslautern-Landau. His contributions to OSCAR center around algebraic schemes.

"My grandmother is manufacturing sculptures and when I was a child, she took me down to her workshop to introduce me to the art of carving, forging, hammering, and giving shape to solid blocks of wood. Attentive observation of the workpiece and exploration of the evolving surfaces, edges, and corners is key for the artist's inner dialog, comparing the intermediate state against the envisioned result. Computer algebra and its applications in algebraic geometry are to me the natural extension of my grandmother's workshop, opening it towards the horizon of what a human mind can possibly grasp as abstract concepts in infinite dimensions and bridging it to ever surprising applications in the sciences and engineering. At the moment this means: work on effective implementations of derived categories of coherent sheaves in OSCAR."

Learn more on his personal website and follow him on GitHub under the username HechtiDerLachs.

New OSCAR Discussion Place

Besides our already existing Slack workspace, there is now a discourse forum for OSCAR. Ask questions, share ideas and help other users. Discourse discussions stay available and searchable, so you may find an answer to your question from searching past discussions. If you cannot find an answer, post your question — the following discussion may help the next person with the same problem. Sign up and join the conversation!

Top 5 Secret OSCAR Tricks

Here is a Top 5 of perhaps not so well-known OSCAR hacks that might save you a lot of time. Thanks to everyone for contributing their favorite tricks!

To multiply two matrices that both contain many zero entries, it can be beneficial to convert them to sparse_matrix and then multiply them using mul_sparse. The final result can be converted back to a (dense) matrix by calling matrix(...). For instance, M1 = sparse_matrix(M1); M2 = sparse_matrix(M2); matrix(mul_sparse(M1, M2)).
Oscar.flatten lets you turn a nested ring like ℚ[x, y][s, t] into the isomorphic flat ring ℚ[x, y, s, t]. For example, given Qxy, (x, y) = QQ[:x, :y]; R, (s, t) = Qxy[:s, :t];, you can call phi = Oscar.flatten(R) to obtain the canonical isomorphism ℚ[x, y][s, t] → ℚ[x, y, s, t]. This enables natural modeling of parameters vs. variables and then switching to the flat representation required e.g. by Gröbner bases and elimination.
Enter $ within an OSCAR shell to activate a polymake session. You can even exchange variables between polymake and OSCAR!
In the very same vein, you can type GAP.prompt() to enter a GAP session within OSCAR.
Use the attribute system (set_attribute! / get_attribute / @attr) to cache expensive computations on objects. After having computed something costly (for instance a Gröbner basis, a Hilbert polynomial, or a singular locus), store it on the object itself: set_attribute!(I, :my_groebner, groebner_basis(I)), and then later get_attribute(I, :my_groebner). Many OSCAR functions already do this internally, and the @attr macro turns a function into an automatically memoized attribute.

OSCAR in the Movies Continues ...

Check out some new OSCAR movie content on tube.mathe. This time, our mascot sloth OSCAR teaches you about Gröbner bases.

You can also find these videos on our YouTube and Instagram channels. Subscribe to help increase our reach!

OSCAR-Shop:

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

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