Welcome to the Sage Reference Manual!

Here you find documentation for all of Sage's features, illustrated with lots of examples. A thematic index follows.

This documentation is licensed under the Creative Commons Attribution-Share Alike 3.0 License.

User Interfaces

Command Line Interface <repl/index>
Jupyter Notebook Interface

Graphics

2D Graphics <plotting/index>
3D Graphics <plot3d/index>

Mathematics

Parents and Categories

Parents and Elements <structure/index>
Coercion <coercion/index>
Categories <categories/index>

Basic Rings and Fields

Integers and Rational Numbers <rings_standard/index>
Real and Complex Numbers <rings_numerical/index>
Commutative Polynomials <polynomial_rings/index>
Power Series and Laurent Series <power_series/index>
Finite Rings and Fields <finite_rings/index>
\\(p\\)-adic Numbers <padics/index>
Noncommutative Polynomials <noncommutative_polynomial_rings/index>
Quaternion Algebras <quat_algebras/index>

Linear Algebra

Matrices and Spaces of Matrices <matrices/index>
Vectors and Modules <modules/index>
Tensors on Free Modules of Finite Rank <tensor_free_modules/index>

Calculus and Analysis

Symbolic Calculus <calculus/index>
Mathematical Constants <constants/index>
Elementary and Special Functions <functions/index>
Asymptotic Expansions <asymptotic/index>
Numerical Optimization <numerical/index>

Probability and Statistics

Probability <probability/index>
Statistics <stats/index>
Quantitative Finance <finance/index>

Mathematical Structures

Sets <sets/index>
Monoids <monoids/index>
Groups <groups/index>
Semirings <semirings/index>
Rings <rings/index>
Algebras <algebras/index>

Discrete Mathematics

Combinatorics <combinat/index>
Graph Theory <graphs/index>
Quivers <quivers/index>
Matroid Theory <matroids/index>
Discrete Dynamics <dynamics/index>
Coding Theory <coding/index>
Cryptography <cryptography/index>
Game Theory <game_theory/index>
Symbolic Logic <logic/index>
SAT solvers <sat/index>

Geometry and Topology

Euclidean Spaces and Vector Calculus <euclidean_spaces/index>
Combinatorial and Discrete Geometry <discrete_geometry/index>
Cell Complexes, Simplicial Complexes, and Simplicial Sets <topology/index>
Manifolds and Differential Geometry <manifolds/index>
Hyperbolic Geometry <hyperbolic_geometry/index>
Parametrized Surfaces <riemannian_geometry/index>
Knot Theory <knots/index>

Homological Algebra

Chain Complexes and their Homology <homology/index>
Resolutions <resolutions/index>

Number Fields, Function Fields, and Valuations

Number Fields <number_fields/index>
Function Fields <function_fields/index>
Discrete Valuations <valuations/index>
Drinfeld Modules <drinfeld_modules/index>

Number Theory

Diophantine Approximation <diophantine_approximation/index>
Quadratic Forms <quadratic_forms/index>
\\(L\\)-Functions <lfunctions/index>
Arithmetic Subgroups of \\({\\rm SL}_2(\\ZZ)\\) <arithgroup/index>
General Hecke Algebras and Hecke Modules <hecke/index>
Modular Forms <modfrm/index>
Modular Symbols <modsym/index>
Modular Abelian Varieties <modabvar/index>

Algebraic and Arithmetic Geometry

Schemes <schemes/index>
Plane and Space Curves <curves/index>
Elliptic and Hyperelliptic Curves <arithmetic_curves/index>

Miscellaneous

Databases <databases/index>
Games <games/index>

Infrastructure

Programming Facilities

Data Structures <data_structures/index>
Utilities <misc/index>
Test Framework <doctest/index>
Parallel Computing <parallel/index>
Python Technicalities <cpython/index>

Subsystem Interfaces

Interpreter Interfaces <interfaces/index>
C/C++ Library Interfaces <libs/index>

Documentation System

Documentation System <documentation/index>

General Information

External Packages <spkg/index>
Bibliographic References <references/index>
History and License <history_and_license/index>

Indices and Tables

genindex
modindex
search