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SymPy 1.11.1 documentation
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SymPy 1.11.1 documentation
  • Installation
  • Tutorials
    • Introductory Tutorial
      • Preliminaries
      • Introduction
      • Gotchas
      • SymPy Features
        • Basic Operations
        • Printing
        • Simplification
        • Calculus
        • Solvers
        • Matrices
        • Advanced Expression Manipulation
      • What’s Next
  • How-to Guides
    • Assumptions
    • Symbolic and fuzzy booleans
    • Writing Custom Functions
    • Solve Equations
      • Solve an equation algebraically
    • Citing SymPy
  • Explanations
    • Gotchas and Pitfalls
    • SymPy Special Topics
      • Finite Difference Approximations to Derivatives
      • Classification of SymPy objects
    • List of active deprecations
  • API Reference
    • Basics
      • Assumptions
        • Ask
        • Assume
        • Refine
        • Predicates
      • Calculus
      • Combinatorics
        • Partitions
        • Permutations
        • Permutation Groups
        • Polyhedron
        • Prufer Sequences
        • Subsets
        • Gray Code
        • Named Groups
        • Nilpotent, Abelian and Cyclic Numbers
        • Utilities
        • Group constructors
        • Test Utilities
        • Tensor Canonicalization
        • Finitely Presented Groups
        • Polycyclic Groups
      • Functions
        • Elementary
        • sympy.functions.elementary.complexes
        • sympy.functions.elementary.trigonometric
        • Trigonometric Functions
        • Trigonometric Inverses
        • sympy.functions.elementary.hyperbolic
        • Hyperbolic Functions
        • Hyperbolic Inverses
        • sympy.functions.elementary.integers
        • sympy.functions.elementary.exponential
        • sympy.functions.elementary.piecewise
        • sympy.functions.elementary.miscellaneous
        • Combinatorial
        • Enumeration
        • Special
      • Integrals
        • Computing Integrals using Meijer G-Functions
        • The G-Function Integration Theorems
        • The Inverse Laplace Transform of a G-function
        • Implemented G-Function Formulae
        • Internal API Reference
        • Integrals
      • Series
        • Series Expansions
        • Sequences
        • Fourier Series
        • Formal Power Series
        • Limits of Sequences
      • Simplify
        • Simplify
        • Hypergeometric Expansion
        • Hongguang Fu’s Trigonometric Simplification
      • Solvers
        • Diophantine
        • Inequality Solvers
        • ODE
        • PDE
        • Solvers
        • Solveset
      • abc
      • Algebras
      • Concrete
      • Core
      • Discrete
      • Numerical Evaluation
      • Numeric Computation
      • Term Rewriting
    • 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)
    • Logic
      • Logic
      • Sets
    • Matrices
      • Matrices
        • Matrices (linear algebra)
        • Common Matrices
        • Dense Matrices
        • Sparse Matrices
        • Sparse Tools
        • Immutable Matrices
        • Matrix Expressions
        • Matrix Normal Forms
      • Tensor
        • N-dim array
        • N-dim array expressions
        • Indexed Objects
        • Methods
        • Tensor
        • Tensor Operators
      • Vector
        • Introduction
        • Basic Implementation details
        • More about Coordinate Systems
        • Scalar and Vector Field Functionality
        • General examples of usage
        • Applications of Vector Integrals
        • Essential Classes in sympy.vector (docstrings)
        • Orienter classes (docstrings)
        • Essential Functions in sympy.vector (docstrings)
    • Number Theory
      • Ntheory Class Reference
      • Ntheory Functions Reference
    • Physics
      • Hydrogen Wavefunctions
      • Matrices
      • Pauli Algebra
      • Quantum Harmonic Oscillator in 1-D
      • Quantum Harmonic Oscillator in 3-D
      • Second Quantization
      • Wigner Symbols
      • Unit systems
        • Philosophy behind unit systems
        • Examples
        • Dimensions and dimension systems
        • Unit prefixes
        • Units and unit systems
        • Physical quantities
      • High energy physics
      • The Physics Vector Module
        • Vector & ReferenceFrame
        • Vector: Kinematics
        • Potential Issues/Advanced Topics/Future Features in Physics/Vector Module
        • Scalar and Vector Field Functionality
        • Essential Classes
        • Kinematics (Docstrings)
        • Printing (Docstrings)
        • Essential Functions (Docstrings)
        • Docstrings for basic field functions
      • Classical Mechanics
        • Masses, Inertias, Particles and Rigid Bodies in Physics/Mechanics
        • Kane’s Method in Physics/Mechanics
        • Lagrange’s Method in Physics/Mechanics
        • Joints Framework in Physics/Mechanics
        • Symbolic Systems in Physics/Mechanics
        • Linearization in Physics/Mechanics
          • Nonminimal Coordinates Pendulum
        • Examples for Physics/Mechanics
          • A rolling disc
            • A rolling disc, with Kane’s method
            • A rolling disc, with Kane’s method and constraint forces
            • A rolling disc using Lagrange’s Method
          • A bicycle
          • Nonminimal Coordinates Pendulum
          • Multi Degree of Freedom Holonomic System
          • A four bar linkage
        • Potential Issues/Advanced Topics/Future Features in Physics/Mechanics
        • References for Physics/Mechanics
        • Autolev Parser
        • SymPy Mechanics for Autolev Users
        • Masses, Inertias & Particles, RigidBodys (Docstrings)
        • Body (Docstrings)
        • Kane’s Method & Lagrange’s Method (Docstrings)
        • Joints Framework (Docstrings)
        • SymbolicSystem (Docstrings)
        • Linearization (Docstrings)
        • Expression Manipulation (Docstrings)
        • Printing (Docstrings)
      • Quantum Mechanics
        • Anticommutator
        • Clebsch-Gordan Coefficients
        • Commutator
        • Constants
        • Dagger
        • Inner Product
        • Tensor Product
        • Cartesian Operators and States
        • Hilbert Space
        • Operator
        • Operator/State Helper Functions
        • Qapply
        • Represent
        • Spin
        • State
        • Circuit Plot
        • Gates
        • Grover’s Algorithm
        • QFT
        • Qubit
        • Shor’s Algorithm
        • Particle in a Box
      • Optics Module
        • Gaussian Optics
        • Medium
        • Polarization
        • Utilities
        • Waves
      • Control Module
        • Control
        • Control API
        • Control System Plots
      • Continuum Mechanics
        • Beam (Docstrings)
        • Solving Beam Bending Problems using Singularity Functions
        • Truss (Docstrings)
    • Utilities
      • Testing
        • pytest
        • Randomised Testing
        • Run Tests
      • Utilities
        • Autowrap Module
        • Codegen
        • Decorator
        • Enumerative
        • Exceptions and Warnings
        • Iterables
        • Lambdify
        • Memoization
        • Miscellaneous
        • PKGDATA
        • Source Code Inspection
        • Timing Utilities
      • Interactive
      • Parsing
      • Printing
    • Topics
      • Geometry
        • Entities
        • Utils
        • Points
        • Lines
        • Curves
        • Ellipses
        • Polygons
        • Plane
      • Holonomic
        • About Holonomic Functions
        • Representation of holonomic functions in SymPy
        • Operations on holonomic functions
        • Converting other representations to holonomic
        • Uses and Current limitations
        • Internal API
      • Lie Algebra
      • Polynomial Manipulation
        • Basic functionality of the module
        • Examples from Wester’s Article
        • Polynomials Manipulation Module Reference
        • AGCA - Algebraic Geometry and Commutative Algebra Module
        • Introducing the Domains of the poly module
        • Reference docs for the Poly Domains
        • Internals of the Polynomial Manipulation Module
        • Series Manipulation using Polynomials
        • Literature
        • Poly solvers
        • Introducing the domainmatrix of the poly module
        • Number Fields
      • Category Theory
      • Cryptography
      • Differential Geometry
      • Plotting
      • Stats
  • Contributing
    • Development Environment Setup
    • Dependencies
    • Build the Documentation
    • Debugging
    • SymPy Docstrings Style Guide
    • Documentation Style Guide
    • Making a Contribution
    • Deprecation Policy
Documentation Version
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SymPy Special Topics#

The purpose of this collection of documents is to provide users of SymPy with topics which are not strictly tutorial or are longer than tutorials and tests. The documents will hopefully fill a gap as SymPy matures and users find more ways to show how SymPy can be used in more advanced topics.

  • Finite Difference Approximations to Derivatives
    • Introduction
    • A Direct Method Using SymPy Matrices
  • Classification of SymPy objects
    • class
    • kind
    • sets and assumptions
    • func
Next
Finite Difference Approximations to Derivatives
Previous
Gotchas and Pitfalls
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Last updated on Jan 30, 2024