Contents

Welcome to Sage’s Reference Manual!

This manual is a thematic index of all of Sage’s features. It also contains many examples that illustrate their use, all of them systematically tested with each release.

Enjoy Sage!

User Interface

• Command Line Interface (REPL)
• Web Notebook

Graphics

• 2D Graphics
• 3D Graphics

Mathematics

Parents, Elements and Categories

• Basic Infrastructure
• Coercion
• Categories

Standard Algebraic Structures

• Monoids
• Groups
• Semirings
• Rings
• Algebras

Standard Rings and Fields

• Integers, Rationals, etc.
• Real and Complex Numbers
• Finite Rings and Fields
• Polynomials
• Formal Power Series
• Algebraic Number Fields
• Function Fields
• p-Adic Numbers
• Quaternion Algebras

Linear Algebra

• Matrices and Spaces of Matrices
• Vectors and Modules
• Tensors on free modules of finite rank

Discrete Mathematics

• Combinatorics
• Graph Theory
• Quivers
• Matroid Theory
• Discrete Dynamics
• Coding Theory
• Game Theory

Calculus

• Symbolic Calculus
• Mathematical Constants
• Elementary and Special Functions

Geometry and Topology

• Combinatorial Geometry
• Cell Complexes and their Homology
• Differential Forms
• Manifolds
• Parametrized Surfaces

Number Theory, Algebraic Geometry

• Diophantine approximation
• Quadratic Forms
• L-Functions
• Schemes
• Elliptic, Plane, and Hyperelliptic Curves
• Arithmetic Subgroups of SL_2(Z)
• General Hecke Algebras and Hecke Modules
• Modular Symbols
• Modular Forms
• Modular Forms for Hecke Triangle Groups
• Modular Abelian Varieties
• Miscellaneous Modular-Form-Related Modules

Logic

• Symbolic Logic
• SAT solvers

Probability and Statistics

• Probability
• Statistics
• Quantitative Finance

Miscellaneous

• Cryptography
• Optimization
• Databases
• Games

Programming

• Data Structures
• Utilities
• Test Framework
• Parallel Computing

Interfaces

• Interpreter Interfaces
• C/C++ Library Interfaces

General Information

• History and License
• Index
• Module Index
• Search Page

This work is licensed under a Creative Commons Attribution-Share Alike 3.0 License.