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
Graphics#
2D Graphics
3D Graphics
Mathematics#
Parents and Categories#
Parents and Elements
Coercion
Categories
Basic Rings and Fields#
Integers and Rational Numbers
Real and Complex Numbers
Commutative Polynomials
Power Series and Laurent Series
Finite Rings and Fields
\(p\)-adic Numbers
Noncommutative Polynomials
Quaternion Algebras
Linear Algebra#
Matrices and Spaces of Matrices
Vectors and Modules
Tensors on Free Modules of Finite Rank
Calculus and Analysis#
Symbolic Calculus
Mathematical Constants
Elementary and Special Functions
Asymptotic Expansions
Numerical Optimization
Probability and Statistics#
Probability
Statistics
Quantitative Finance
Mathematical Structures#
Sets
Monoids
Groups
Semirings
Rings
Algebras
Discrete Mathematics#
Combinatorics
Graph Theory
Quivers
Matroid Theory
Discrete Dynamics
Coding Theory
Cryptography
Game Theory
Symbolic Logic
SAT solvers
Geometry and Topology#
Euclidean Spaces and Vector Calculus
Combinatorial and Discrete Geometry
Cell Complexes, Simplicial Complexes, and Simplicial Sets
Hyperbolic Geometry
Parametrized Surfaces
Knot Theory
Homological Algebra#
Chain Complexes and their Homology
Resolutions
Number Fields, Function Fields, and Valuations#
Number Fields
Function Fields
Discrete Valuations
Number Theory#
Diophantine approximation
Quadratic Forms
\(L\)-Functions
Arithmetic Subgroups of \({\rm SL}_2(\ZZ)\)
General Hecke Algebras and Hecke Modules
Modular Symbols
Modular Forms
Quasimodular Forms
Modular Forms for Hecke Triangle Groups
Modular Abelian Varieties
Miscellaneous Modular-Form-Related Modules
Algebraic and Arithmetic Geometry#
Schemes
Plane and Space Curves
Elliptic and Hyperelliptic Curves
Miscellaneous#
Databases
Games
Programming#
Facilities#
Data Structures
Utilities
Test Framework
Parallel Computing
Interfaces#
Interpreter Interfaces
C/C++ Library Interfaces
Python Technicalities
Documentation System#
Documentation System
General Information#
History and License