Reference Manual

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# 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
- Jupyter Notebook 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
- Modules over Ore rings

### Calculus and Analysis

- Symbolic Calculus
- Mathematical Constants
- Elementary and Special Functions
- Asymptotic Expansions
- Numerical Optimization

### Probability and Statistics

- Probability
- Statistics

### 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
- Manifolds and Differential Geometry
- 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
- Drinfeld Modules

### Number Theory

- Diophantine Approximation
- Quadratic Forms
- \(L\)-Functions
- Arithmetic Subgroups of \({\rm SL}_2(\ZZ)\)
- General Hecke Algebras and Hecke Modules
- Modular Forms
- Modular Symbols
- Modular Abelian Varieties

### Algebraic and Arithmetic Geometry

- Schemes
- Plane and Space Curves
- Elliptic and Hyperelliptic Curves

### Miscellaneous

- Databases
- Games

## Infrastructure

### Programming Facilities

- Data Structures
- Utilities
- Test Framework
- Parallel Computing
- Python Technicalities

### Subsystem Interfaces

- Interpreter Interfaces
- C/C++ Library Interfaces

### Documentation System

- Documentation System

## General Information

- External Packages
- Bibliographic References
- History and License