passagemath-categories 10.5.29

passagemath: Sage categories and basic rings

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 2005-2025 under the motto “Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, and MATLAB”.

The passagemath fork was created in October 2024 with the following goals:

• providing modularized installation with pip, thus completing a major project started in 2020 in the Sage codebase,

• establishing first-class membership in the scientific Python ecosystem,

• giving clear attribution of upstream projects,

• providing independently usable Python interfaces to upstream libraries,

• providing platform portability and integration testing services to upstream projects,

• inviting collaborations with upstream projects,

• building a professional, respectful, inclusive community,

• developing a port to Pyodide for serverless deployment with Javascript,

• developing a native Windows port.

Full documentation is available online.

passagemath attempts to support all major Linux distributions and recent versions of macOS. Use on Windows currently requires the use of Windows Subsystem for Linux or virtualization.

Complete sets of binary wheels are provided on PyPI for Python versions 3.9.x-3.12.x. Python 3.13.x is also supported, but some third-party packages are still missing wheels, so compilation from source is triggered for those.

About this pip-installable distribution package

The pip-installable distribution package sagemath-categories is a distribution of a small part of the Sage Library.

It provides a small subset of the modules of the Sage library (“sagelib”, sagemath-standard) that is a superset of sagemath-objects (providing Sage objects, the element/parent framework, categories, the coercion system and the related metaclasses), making various additional categories available without introducing dependencies on additional mathematical libraries.

What is included

• Structure, Coercion framework, Base Classes, Metaclasses

• Categories and functorial constructions

• Sets

• Basic Combinatorial and Data Structures: Binary trees, Bitsets, Permutations, Combinations

• Basic Rings and Fields: Integers, Rationals, Double Precision Reals, Z/nZ

• Commutative Polynomials, Power Series and Laurent Series, Rational Function Fields

• Arithmetic Functions, Elementary and Special Functions as generic entry points

• Base classes for Groups, Rings, Finite Fields, Number Fields, Schemes

• Facilities for Parallel Computing, Formatted Output

Available in other distribution packages

• sagemath-combinat: Algebraic combinatorics, combinatorial representation theory

• sagemath-graphs: Graphs, posets, hypergraphs, designs, abstract complexes, combinatorial polyhedra, abelian sandpiles, quivers

• sagemath-groups: Groups, invariant theory

• sagemath-modules: Vectors, matrices, tensors, vector spaces, affine spaces, modules and algebras, additive groups, quadratic forms, root systems, homology, coding theory, matroids

• sagemath-plot: Plotting and graphics with Matplotlib, Three.JS, etc.

• sagemath-polyhedra: Convex polyhedra in arbitrary dimension, triangulations, polyhedral fans, lattice points, geometric complexes, hyperplane arrangements

• sagemath-repl: IPython REPL, the interactive language of SageMath (preparser), interacts, development tools

• sagemath-schemes: Schemes, varieties, Groebner bases, elliptic curves, algebraic Riemann surfaces, modular forms, arithmetic dynamics

• sagemath-symbolics: Symbolic expressions, calculus, differentiable manifolds, asymptotics

Dependencies

When building from source, development packages of gmp, mpfr, and mpc are needed.