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passagemath: Algorithms for Rubik’s cube

passagemath is open source mathematical software in Python, released under the GNU General Public Licence GPLv2+.

It is a fork of SageMath, which has been developed 2005-2026 under the motto “Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, and MATLAB”.

The passagemath fork uses the motto “Creating a Free Passage Between the Scientific Python Ecosystem and Mathematical Software Communities.” It was created in October 2024 with the following goals:

providing modularized installation with pip from binary wheels, - this major project was started in May 2020 in the Sage codebase and completed in passagemath 10.5.29 (May 2025),
establishing first-class membership in the scientific Python ecosystem,
giving clear attribution of upstream projects,
providing independently usable Python interfaces to upstream libraries,
offering platform portability and integration testing services to upstream projects,
inviting collaborations with upstream projects,
building a professional, respectful, inclusive community,
empowering Sage users to participate in the scientific Python ecosystem by publishing packages,
developing a port to WebAssembly (Pyodide, emscripten-forge) for serverless deployment with Javascript,
developing a native Windows port - passagemath 10.6.1 (July 2025) published the first pip-installable wheel packages for native Windows on x86_64, - passagemath packages became available in the [MSYS2 software distribution](https://packages.msys2.org/search?t=pkg&q=passagemath) in November 2025.

Moreover, the passagemath project:

provides a stable, frequently updated version of the Sage distribution,
integrates additional mathematical software, notably Macaulay2, a full set of GAP packages, and the Combinatorial Matrix Recognition library,
curates a library of Sage user packages.

Full documentation is available online.

passagemath attempts to support and provides binary wheels suitable for all major Linux distributions and recent versions of macOS.

Binary wheels for native Windows (x86_64, ARM) are are available for a subset of the passagemath distributions. Use of the full functionality of passagemath on Windows currently requires the use of Windows Subsystem for Linux (WSL) or virtualization.

The supported Python versions in the passagemath-10.8.x series are 3.11.x-3.14.x; the passagemath-10.10.x series is adding support for Python 3.15.

About this pip-installable distribution package

This pip-installable distribution passagemath-rubiks provides an interface to several programs for working with Rubik’s cubes.

Michael Reid (GPL) http://www.cflmath.com/~reid/Rubik/optimal_solver.html

optimal - uses many pre-computed tables to find an optimal solution to the 3x3x3 Rubik’s cube

Dik T. Winter (MIT License)

cube - uses Kociemba’s algorithm to iteratively find a short solution to the 3x3x3 Rubik’s cube
size222 - solves a 2x2x2 Rubik’s cube

Eric Dietz (GPL) https://web.archive.org/web/20121212175710/http://www.wrongway.org/?rubiksource

cu2 - A fast, non-optimal 2x2x2 solver
cubex - A fast, non-optimal 3x3x3 solver
mcube - A fast, non-optimal 4x4x4 solver

What is included

Interface
Features (via passagemath-environment)
Binary wheels on PyPI contain prebuilt copies of rubiks executables.

Examples

Using rubiks programs on the command line:

$ pipx run --spec "passagemath-rubiks" sage -sh -c cubex

Finding the installation location of a rubiks program:

$ pipx run --spec "passagemath-rubiks[test]" ipython

In [1]: from sage.features.rubiks import cubex

In [2]: cubex().absolute_filename()

Using the Python interface:

$ pipx run --spec "passagemath-rubiks[test]" ipython

In [1]: from sage.interfaces.rubik import *

In [2]: C = RubiksCube("R U F L B D")

In [3]: sol = CubexSolver().solve(C.facets()); sol
Out[3]: "U' L' L' U L U' L U D L L D' L' D L' D' L D L' U' L D' L' U L' B' U' L' U B L D L D' U' L' U L B L B' L' U L U' L' F' L' F L' F L F' L' D' L' D D L D' B L B' L B' L B F' L F F B' L F' B D' D' L D B' B' L' D' B U' U' L' B' D' F' F' L D F'"

Using sage.groups.perm_gps:

$ pipx run --spec "passagemath-rubiks[test]" ipython

In [1]: from passagemath_rubiks import *

In [2]: rubik = CubeGroup(); state = rubik.faces("R")

In [3]: rubik.solve(state)
Out[3]: 'R'

Metadata

Release files for passagemath-rubiks 10.8.14rc2

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Source distribution for passagemath-rubiks 10.8.14rc2
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10.8.14rc2 This release

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