passagemath-categories 10.4.5

passagemath: Sage categories and basic rings

About SageMath

“Creating a Viable Open Source Alternative to

Magma, Maple, Mathematica, and MATLAB”

Copyright (C) 2005-2024 The Sage Development Team

https://www.sagemath.org

SageMath fully supports all major Linux distributions, recent versions of macOS, and Windows (Windows Subsystem for Linux).

See https://doc.sagemath.org/html/en/installation/index.html for general installation instructions.

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.