Tutorials

Explore Jupyter notebooks demonstrating OSCAR’s capabilities. The tutorials are designed for, and tested with, the latest stable release OSCAR v1.7.2.

Before You Start

To avoid compatibility issues, make sure you’re using OSCAR v1.7.2 (upgrade instructions).

If you have not yet installed OSCAR, follow our installation guide.

Running Tutorials Locally

1. Download the notebook of interest from the list below.
2. Launch Jupyter on your machine (see Jupyter documentation).
3. Open the downloaded notebook, and execute it using a Julia kernel.

Available Tutorials

Commutative Algebra

FTheoryTools

Group Theory

Intersection Theory

Linear Algebra

Number Theory

Polyhedral Geometry

Schemes

Toric Geometry

A computation with multisymmetric polynomials

Author(s): Daniele Agostini, Jinhyung Park

Last modified: 28 Oct 2025

Topic: Commutative Algebra

Computations with Binomial Ideals

Author(s): Wolfram Decker, Clara Petroll

Last modified: 15 May 2024

Topic: Commutative Algebra

How to solve multivariate polynomial systems of equations in Oscar

Author(s): Christian Eder

Last modified: 10 Sep 2025

Topic: Commutative Algebra

Polynomial Rings

Author(s): John Abbott, Martin Bies, Luca Remke, Hans Schönemann

Last modified: 12 Jul 2024

Topic: Commutative Algebra

Parametrize the volume of slices

Author(s): Chiara Meloni

Last modified: 15 Mar 2024

Topic: Polyhedral Geometry

Polyhedral Geometry

Author(s): Martin Bies, Luca Remke

Last modified: 12 Jul 2024

Topic: Polyhedral Geometry

Computing Cox rings of linear quotients

Author(s): Johannes Schmitt

Last modified: 15 Mar 2024

Topic: Toric Geometry

Cox rings of blow-ups of points

Author(s): Mara Belotti

Last modified: 05 Jul 2024

Topic: Toric Geometry

Toric geometry

Author(s): Martin Bies, Luca Remke

Last modified: 03 Mar 2025

Topic: Toric Geometry

F-Theory Tools

Author(s): Martin Bies, Andrew P. Turner

Last modified: 12 Jul 2024

Topic: FTheoryTools

F-Theory Tools -- Advanced Functionality

Author(s): Martin Bies, Andrew P. Turner, Mikelis E. Mikelson

Last modified: 15 Sep 2025

Topic: FTheoryTools

Elliptic Fibrations and Covered Schemes

Author(s): Simon Brandhorst, Matthias Zach

Last modified: 02 Aug 2024

Topic: Schemes

Introduction to Number Fields: Towers

Author(s): Claus Fieker

Last modified: 04 Apr 2024

Topic: Number Theory

Quadratic lattices

Author(s): Tommy Hofmann

Last modified: 15 Sep 2025

Topic: Number Theory

Combinatorics of Hurwitz numbers

Author(s): Victoria Schleis

Last modified: 15 Mar 2024

Topic: Intersection Theory

Intersection Product on the Cartesian Product of a Curve

Author(s): Daniele Agostini, Daniel Plaumann, Rainer Sinn, Yannik Wesner

Last modified: 19 Sep 2025

Topic: Intersection Theory

A question of Pham Huu Tiep about a group of symplectic type

Author(s): Thomas Breuer

Last modified: 22 Sep 2025

Topic: Group Theory

Analyzing Rubik's Cube

Author(s): Martin Schönert (translated to OSCAR by Thomas Breuer)

Last modified: 24 Jun 2024

Topic: Group Theory

Generation of sporadic simple groups by 𝜋- and 𝜋'-subgroups

Author(s): Thomas Breuer

Last modified: 12 Apr 2024

Topic: Group Theory

Irreducible representations of a finite abelian group over a finite field

Author(s): Thomas Breuer

Last modified: 17 Oct 2025

Topic: Group Theory

Perfect central extensions of PSL(3,4) in the Monster group

Author(s): Thomas Breuer

Last modified: 12 Apr 2024

Topic: Group Theory

Linear Algebra

Author(s): Martin Bies, Aaruni Kaushik

Last modified: 19 Nov 2025

Topic: Linear Algebra

Tutorial grid last updated on 06 May 2026.

More Tutorial Resources

Looking for more resources? Check out the polymake notebooks and Hecke notebooks.

Contributing Tutorials

Want to improve or add a tutorial? See our contribution guidelines.