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:

• abc
  • Caveats
  • Examples
• Algebras
  • Introduction
  • Quaternion Reference
• Assumptions
  • Predicate
  • Querying
  • Contents
  • Performance improvements
  • Misc
• Calculus
  • Singularities
  • Finite difference weights
• Category Theory
  • Introduction
  • Base Class Reference
  • Diagram Drawing
• Code Generation
  • 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)
• Combinatorics
  • Contents
• Concrete
  • Hypergeometric terms
  • Concrete Class Reference
  • Concrete Functions Reference
• Core
  • sympify
  • assumptions
  • cache
  • basic
  • core
  • singleton
  • expr
  • symbol
  • numbers
  • power
  • mul
  • add
  • mod
  • relational
  • multidimensional
  • function
  • evalf
  • containers
  • compatibility
  • exprtools
  • kind
• Cryptography
• Differential Geometry
  • Introduction
  • Base Class Reference
• Diophantine
  • Diophantine equations
  • Module structure
  • Tutorial
  • References
  • User Functions
  • Internal Functions
  • Internal Classes
• Discrete
  • Transforms
  • Convolutions
• Numerical Evaluation
  • Basics
  • Floating-point numbers
  • Accuracy and error handling
  • Sums and integrals
  • Numerical simplification
• Functions
  • Contents
• Geometry
  • Introduction
  • Available Entities
  • Example Usage
  • Intersection of medians
  • An in-depth example: Pappus’ Hexagon Theorem
  • Miscellaneous Notes
  • Future Work
• Holonomic
  • Contents
• Inequality Solvers
• Integrals
  • Examples
  • Integral Transforms
  • Internals
  • API reference
  • TODO and Bugs
  • References
  • Examples
  • For 2D Polygons
  • For 3-Polytopes/Polyhedra
  • API reference
• Computing Integrals using Meijer G-Functions
  • Overview
  • Polar Numbers and Branched Functions
  • Representing Branched Functions on the Argand Plane
  • Table Lookups and Inverse Mellin Transforms
  • Applying the Integral Theorems
• The G-Function Integration Theorems
  • Conditions of Convergence for Integral (1)
  • Conditions of Convergence for Integral (2)
• The Inverse Laplace Transform of a G-function
  • How to compute the integral
  • When this computation is valid
  • When the integral exists
• Implemented G-Function Formulae
• Internal API Reference
• Interactive
  • Session
  • Printing
• Lie Algebra
• Logic
  • Introduction
  • Forming logical expressions
  • Boolean functions
  • Simplification and equivalence-testing
  • Inference
• Matrices
  • Matrices (linear algebra)
  • Common Matrices
  • Dense Matrices
  • Sparse Matrices
  • Sparse Tools
  • Immutable Matrices
  • Matrix Expressions
• Number Theory
  • Ntheory Class Reference
  • Ntheory Functions Reference
• Numeric Computation
  • Subs/evalf
  • Lambdify
  • uFuncify
  • Aesara
  • So Which Should I Use?
• ODE
  • User Functions
  • Hint Functions
  • Lie heuristics
  • Rational Riccati Solver
  • System of ODEs
  • Information on the ode module
• Parsing
  • Parsing Functions Reference
  • Parsing Transformations Reference
  • Experimental \(\mathrm{\LaTeX}\) Parsing
  • \(\mathrm{\LaTeX}\) Parsing Caveats
  • \(\mathrm{\LaTeX}\) Parsing Functions Reference
  • \(\mathrm{\LaTeX}\) Parsing Exceptions Reference
  • SymPy Expression Reference
  • Runtime Installation
• PDE
  • User Functions
  • Hint Methods
  • Information on the pde module
• Physics
  • Contents
• Plotting
  • Introduction
  • Plot Class
  • Plotting Function Reference
  • PlotGrid Class
  • Series Classes
  • Backends
  • Pyglet Plotting
  • Plot Window Controls
  • Coordinate Modes
  • Specifying Intervals for Variables
  • Using the Interactive Interface
  • Using Custom Color Functions
  • Plotting Geometric Entities
  • Plotting with ASCII art
• Polynomial Manipulation
  • Contents
• Printing
  • Printer Class
  • PrettyPrinter Class
  • C code printers
  • C++ code printers
  • RCodePrinter
  • Fortran Printing
  • Mathematica code printing
  • Maple code printing
  • Javascript Code printing
  • Julia code printing
  • Octave (and Matlab) Code printing
  • Rust code printing
  • Aesara Code printing
  • Gtk
  • LambdaPrinter
  • LatexPrinter
  • MathMLPrinter
  • PythonCodePrinter
  • PythonPrinter
  • srepr
  • StrPrinter
  • Tree Printing
  • Preview
  • Implementation - Helper Classes/Functions
  • Pretty-Printing Implementation Helpers
  • dotprint
• Term Rewriting
  • Expanding
  • Common Subexpression Detection and Collection
• Series
  • Contents
• Sets
  • Basic Sets
  • Elementary Sets
  • Compound Sets
  • Singleton Sets
  • Special Sets
  • Power sets
  • Condition Sets
• Simplify
  • Simplify
  • Hypergeometric Expansion
  • Hongguang Fu’s Trigonometric Simplification
• 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
• 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)
• Stats
  • Examples
  • Random Variable Types
  • Interface
  • Mechanics
• Tensor
  • Contents
• Testing
  • pytest
  • Randomised Testing
  • Run Tests
• Utilities
  • Autowrap Module
  • Codegen
  • Decorator
  • Enumerative
  • Iterables
  • Lambdify
  • Memoization
  • Miscellaneous
  • PKGDATA
  • Source Code Inspection
  • Timing Utilities
• Vector
  • Guide to Vector
  • Vector API
  • References for Vector

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).