SymPy Modules Reference

Because every feature of SymPy must have a test case, when you are not sure how to use something, just look into the tests/ directories, find that feature and read the tests for it, that will tell you everything you need to know.

Most of the things are already documented though in this document, that is automatically generated using SymPy’s docstrings.

Click the “modules” (Module Index) link in the top right corner to easily access any SymPy module, or use the list below:

• SymPy Core
  • sympify
  • assumptions
  • cache
  • basic
  • core
  • singleton
  • expr
  • Expr
  • UnevaluatedExpr
  • AtomicExpr
  • symbol
  • numbers
  • power
  • mul
  • add
  • mod
  • relational
  • multidimensional
  • function
  • evalf
  • containers
  • compatibility
  • exprtools
• Combinatorics Module
  • Contents
• Number Theory
  • Ntheory Class Reference
  • Ntheory Functions Reference
• Basic Cryptography Module
• Concrete Mathematics
  • Hypergeometric terms
  • Concrete Class Reference
  • Concrete Functions Reference
• Discrete Module
  • Transforms
  • Convolutions
• Numerical evaluation
  • Basics
  • Floating-point numbers
  • Accuracy and error handling
  • Sums and integrals
  • Numerical simplification
• Structural Details of Code Generation with SymPy
  • Introduction
  • Code printers (sympy.printing)
  • Codegen (sympy.utilities.codegen)
  • Autowrap
  • Classes and functions for rewriting expressions (sympy.codegen.rewriting)
  • Tools for simplifying expressions using approximations (sympy.codegen.approximations)
  • Classes for abstract syntax trees (sympy.codegen.ast)
  • Special C math functions (sympy.codegen.cfunctions)
  • C specific AST nodes (sympy.codegen.cnodes)
  • C++ specific AST nodes (sympy.codegen.cxxnodes)
  • Fortran specific AST nodes (sympy.codegen.fnodes)
  • Algorithms (sympy.codegen.algorithms)
  • Python utilities (sympy.codegen.pyutils)
  • C utilities (sympy.codegen.cutils)
  • Fortran utilities (sympy.codegen.futils)
• Numeric Computation
  • Subs/evalf
  • Lambdify
  • uFuncify
  • Theano
  • So Which Should I Use?
• Functions Module
  • Contents
• Geometry Module
  • Introduction
  • Available Entities
  • Example Usage
  • Intersection of medians
  • An in-depth example: Pappus’ Hexagon Theorem
  • Miscellaneous Notes
  • Future Work
• Holonomic Functions
  • Contents
• Symbolic Integrals
  • Examples
  • Integral Transforms
  • Internals
  • API reference
  • TODO and Bugs
• Numeric Integrals
• Integration over Polytopes
  • References
  • Examples
  • For 2D Polygons
  • For 3-Polytopes/Polyhedra
  • API reference
• Lie Algebra Module
• Logic Module
  • Introduction
  • Forming logical expressions
  • Boolean functions
  • Simplification and equivalence-testing
  • Inference
• Matrices
  • Matrices (linear algebra)
  • Common Matrices
  • Dense Matrices
  • Sparse Matrices
  • Immutable Matrices
  • Matrix Expressions
• Polynomials Manipulation Module
  • Contents
• Printing System
  • Printer Class
  • PrettyPrinter Class
  • C code printers
  • C++ code printers
  • RCodePrinter
  • Fortran Printing
  • Mathematica code printing
  • Javascript Code printing
  • Julia code printing
  • Octave (and Matlab) Code printing
  • Rust code printing
  • Theano Code printing
  • Gtk
  • LambdaPrinter
  • LatexPrinter
  • MathMLPrinter
  • PythonCodePrinter
  • PythonPrinter
  • srepr
  • StrPrinter
  • Tree Printing
  • Preview
  • Implementation - Helper Classes/Functions
  • Pretty-Printing Implementation Helpers
  • dotprint
• Plotting Module
  • Introduction
  • Plot Class
  • Plotting Function Reference
  • Series Classes
• Pyglet Plotting Module
  • Plot Window Controls
  • Coordinate Modes
  • Specifying Intervals for Variables
  • Using the Interactive Interface
  • Using Custom Color Functions
  • Plotting Geometric Entities
• Assumptions Module
  • Contents
  • Querying
  • Design
  • Extensibility
  • Performance improvements
  • Misc
• Term rewriting
  • Expanding
  • Common Subexpression Detection and Collection
• Series Module
  • Contents
• Sets
  • Set
  • Interval
  • FiniteSet
  • Union
  • Intersection
  • ProductSet
  • Complement
  • EmptySet
  • UniversalSet
  • Naturals
  • Naturals0
  • Integers
  • ImageSet
  • Range
  • ComplexRegion
• Simplify
  • simplify
  • separatevars
  • nthroot
  • besselsimp
  • hypersimp
  • hypersimilar
  • nsimplify
  • posify
  • logcombine
  • Radsimp
  • Ratsimp
  • Trigonometric simplification
  • Power simplification
  • Combinatorial simplification
  • Square Root Denesting
  • Common Subexpression Elimination
  • Hypergeometric Function Expansion
  • Traversal Tools
  • EPath Tools
• Details on the Hypergeometric Function Expansion Module
  • Hypergeometric Function Expansion Algorithm
  • Meijer G-Functions of Finite Confluence
  • Extending The Hypergeometric Tables
  • Implemented Hypergeometric Formulae
  • References
• Stats
  • Examples
  • Random Variable Types
  • Interface
  • Mechanics
• ODE
  • User Functions
  • Hint Functions
  • Lie heuristics
  • System of ODEs
  • Information on the ode module
• PDE
  • User Functions
  • Hint Methods
  • Information on the pde module
• Solvers
  • Algebraic equations
  • Ordinary Differential equations (ODEs)
  • Partial Differential Equations (PDEs)
  • Deutils (Utilities for solving ODE’s and PDE’s)
  • Recurrence Equations
  • Systems of Polynomial Equations
  • Diophantine Equations (DEs)
  • Inequalities
• Diophantine
  • Diophantine equations
  • Module structure
  • Tutorial
  • References
  • User Functions
  • Internal Functions
• Inequality Solvers
• Solveset
  • What’s wrong with solve():
  • Why Solveset?
  • Why do we use Sets as an output type?
  • Input API of solveset
  • What is this domain argument about?
  • What are the general methods employed by solveset to solve an equation?
  • How do we manipulate and return an infinite solution?
  • How does solveset ensure that it is not returning any wrong solution?
  • Search based solver and step-by-step solution
  • How do we deal with cases where only some of the solutions are known?
  • What will you do with the old solve?
  • How are symbolic parameters handled in solveset?
  • References
  • Solveset Module Reference
  • linear_eq_to_matrix
  • linsolve
  • nonlinsolve
  • transolve
  • Diophantine Equations (DEs)
  • Inequalities
  • Ordinary Differential equations (ODEs)
  • Partial Differential Equations (PDEs)
• Tensor Module
  • Contents
• Utilities
  • Autowrap Module
  • Codegen
  • Decorator
  • Enumerative
  • Iterables
  • Lambdify
  • Memoization
  • Miscellaneous
  • PKGDATA
  • pytest
  • Randomised Testing
  • Run Tests
  • Source Code Inspection
  • Timing Utilities
• Parsing input
  • Parsing Functions Reference
  • Parsing Transformations Reference
  • Experimental \(\LaTeX\) Parsing
  • \(\LaTeX\) Parsing Caveats
  • \(\LaTeX\) Parsing Functions Reference
  • \(\LaTeX\) Parsing Exceptions Reference
  • Runtime Installation
• Calculus
  • Singularities
  • Finite difference weights
• Physics Module
  • Contents
• Category Theory Module
  • Introduction
  • Base Class Reference
  • Diagram Drawing
• Differential Geometry Module
  • Introduction
  • Base Class Reference
• Vector Module
  • Guide to Vector
  • Vector API
  • References for Vector
• Algebras Module
  • Introduction
  • Quaternion Reference

Contributions to docs

All contributions are welcome. If you’d like to improve something, look into the sources if they contain the information you need (if not, please fix them), otherwise the documentation generation needs to be improved (look in the doc/ directory).